Books:

1. The Topological Classification of Stratified Spaces, University of Chicago Press 1994 (errata) BAMS review

2. Tel Aviv Topology Conference: Rothenberg Festschrift, Contemporary Math 231 (1999), edited with Michael Farber and Wolfgang Lueck

3. Computers, Rigidity, and Moduli: The Large Scale Geometry of Riemannian Moduli Space (2005, Princeton University Press)

4. Numbers and Stuff (2010 Draft; please send me comments, especially if you use it in a class or read it yourself!)

Published Articles and Preprints

Math reviews of earlier papers

Abstracts of some recent papers and other remarks

1. Homotopy equivalent manifolds by pasting. Current trends in algebraic topology, Part 2 (London, Ont., 1981), pp. 423-433, CMS Conf. Proc., 2, Amer. Math. Soc., Providence, R.I.

2. There exist finitely presented groups with infinite ooze. Duke Math. J. 49 (1982), no. 4, 1129-1133.

3. Constructions of group actions a survey of some recent developments, Group actions on manifolds (Boulder, Colo., 1983), 269--298, Contemp. Math. 36

4. Oliver's formula and Minkowski's theorem. Algebraic and geometric topology (New Brunswick, N.J., 1983), 420-421, Lecture Notes in Math., 1126

5. Some nilpotent complexes. in Algebraic and geometric topology (New Brunswick, N.J., 1983), 422-423, Lecture Notes in Math., 1126

6. The Novikov conjecture and low-dimensional topology. Comment. Math. Helv. 58 (1983), no. 3, 355-364.

7. Constructing homotopy equivalences. Topology 23 (1984), no. 3, 347-379.

8. Caracteristiques d'Euler et groupes fondamentaux des varietes de dimension 4. Comment. Math. Helv. 60 (1985), no. 1, 139-144. (with Hausmann)

9. Improving homological triviality. Comm. Pure Appl. Math. 38 (1985), no. 6, 911-917.

10. A geometric interpretation of Siebenmann's periodicity phenomenon Geometry and topology (Athens, Ga., 1985), 47-52, Lecture Notes in Pure and Appl. Math., 105, Dekker, New York. (with Cappell)

11. Continuous versus discrete symmetry. in Geometry and topology (Athens, Ga., 1985), 319-323, Lecture Notes in Pure and Appl. Math., 105, Dekker, New York,

12. Group actions and higher signatures. Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no. 5, 1297-1298.

13. Parallelizability of finite H-spaces. Comment. Math. Helv. 60 (1985), no. 4, 628-629. (with Cappell)

14. Group actions on homology spheres. Invent. Math 86 (1986), no. 2, 209-231. (with Davis)

15. Homologically trivial group actions. I. Simply connected manifolds. Amer. J. Math. 108 (1986), no. 5, 1005-1021.

16. Homologically trivial group actions. II. Nonsimply connected manifolds. Amer. J. Math. 108 (1986), no. 6, 1259-1275.

17. Group actions and higher signatures. II. Comm. Pure Appl. Math. 40 (1987), no. 2, 179-187.

18. Homology propagation of group actions, Comm. Pure Appl. Math 40 (1987), no. 6, 723-744. (with Cappell)

19. Free Q/Z actions. Comment. Math. Helv. 62 (1987), no. 3, 450- 464.

20. On fibering four- and five-manifolds. Israel J. Math 59 (1987), no. 1, 1-7.

21. Group actions and equivariant Lipschitz analysis. (with Rothenberg) Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 109-112.

22. The Lipschitz rationality of linear representations. Comm. Pure Appl. Math. 40 (1987), no. 5, 609-610.

23. Aspects of the Novikov conjecture. Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988), 281-297, Contemp. Math., 105.

24. Which H-spaces are manifolds? I. (with Cappell) Topology 27 (1988), no. 4, 377-386.

25. Higher G-indices and applications. (with Rosenberg) Ann. Sci. Ecole Norm. Sup. (4) 21 (1988), no. 4, 479-495.

26. Class numbers, the Novikov conjecture, and transformation groups. Topology 27 (1988), no. 3, 353-365.

27. Homotopy invariance of Eta-invariants. Proc. Nat. Acad. Sci. U.S.A. 85 (1988), no. 15, 5362-5363.

28. Phenomenes de rigidite topologique equivariante. C. R. Acad. Sci. Paris Ser. I Math. 306 (1988), no. 19, 777-782. (with Ferry and Rosenberg)

29. Semifree locally linear PL actions on the sphere. Israel J. Math. 66 (1989), no. 1-3, 351-363.

30. Finite detection of compact actions. I. Comm. Pure Appl. Math. 42 (1989), no. 3, 299 -307. Erratum: `Comm. Pure Appl. Math. 42 (1989), no. 5, 709.

31. G-signatures and cyclotomic units, Proceedings of the 1987 Georgia Topology Conference (Athens, GA, 1987). Topology Appl. 32 (1989), no. 2, 183-196.

32. On smooth surgery. Comm. Pure Appl. Math. 43 (1990), no. 5, 695-696.

33. All finite groups act on fake complex projective spaces. Proc. Amer. Math. Soc. 110 (1990), no. 1, 259-261.

34. An equivariant Novikov conjecture. With an appendix by J. P. May. K-Theory 4 (1990), no. 1, 29-53. (with Rosenberg)

35. The classification of nonlinear similarities over Z2r. Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 1, 51-57. (with Cappell, Shaneson, Steinberger and West))

36. Curvature, tangentiality, and controlled topology. Invent. Math 105 (1991), no. 2, 401-414. (with Ferry)

37. Classes topologiques caracteristiques pour les actions de groupes sur les espaces singuliers. C. R. Acad. Sci. Paris Ser. I Math. 313 (1991), no. 5, 293-295. (with Cappell and Shaneson)

38. Classification de certains espaces stratifies. C. R. Acad. Sci. Paris Ser. I Math. 313 (1991), no. 6, 399-401. (with Cappell)

39. A simple construction of Atiyah-Singer classes and piecewise linear transformation groups. J. Differential Geom. 33 (1991), no. 3, 731-742. (with Cappell)

40. Aperiodic tilings, positive scalar curvature and amenability of spaces. J. Amer. Math. Soc. 5 (1992), no. 4, 907-918. (with Block)

41. Characteristic classes and distortion of diffeomorphisms. J. Amer. Math. Soc. 5 (1992), no. 4, 919-921. (with Attie and Block)

42. Higher G-signatures for Lipschitz manifolds K-Theory 7 (1993), no. 2, 101-132. (with Rosenberg)

43. Topology of homology manifolds. Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 324-328. (with Bryant, Ferry and Mio)

44. Homotopy invariance of Novikov-Shubin invariants and $L\sp 2$ Betti numbers. Proc. Amer. Math. Soc., 125 (1997), no. 12, 3757-3762. (with Block and Mathai)

45. Large scale homology and geometry, AMS/IP Studies in Advanced Mathematics, 2(1997) 522-569 (with Block)

46. Topology of homology manifolds. Ann. of Math. (2) 143 (1996), no. 3, 435 - 467 (with J.Bryant, S.Ferry and W.Mio)

47. Replacement of fixed sets and of their normal representations in transformation groups of manifolds. Prospects in topology (Princeton, NJ, 1994), 67-109, Ann. of Math. Stud., 138, Princeton Univ. Press, Princeton, NJ, 1995 (with Cappell)

48. Obstructions to propagation of group actions. Bol. Soc. Mat. Mexicana (3) 2 (1996), no. 1, 1-14. (with Davis)

49. Characteristic fixed point sets for group actions on the sphere, Comm Pure and Applied Math 52 (1999), no. 8, 935-947. (with Davis)

50. Rationality of $\rho$-invariants. appendix to Jumps of the eta- invariant. by Farber and Levine, Math. Z. 223 (1996), no. 2, 197-246

51. A coarse approach to the Novikov conjecture. (with Ferry) Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993), 147-163, London Math. Soc. Lecture Note Ser., 226, Cambridge Univ. Press, Cambridge, 1995.

52. Discrete circle actions: a note using non-standard analysis. Israel J. Math. 94 (1996), 147-155. (with Manevitz) Erratum.

53. Algorithmic unsolvability of the triviality problem for multidimensional knots. Comment. Math. Helv. 71 (1996), no. 3, 426 - 434. (with Nabutovsky)

54. On the homotopy invariance of the boundedly controlled analytic signature of a manifold over an open cone. (with Pederson and Roe) Novikov conjectures, index theorems and rigidity, Vol. 2 (Oberwolfach, 1993), 285-300, London Math. Soc. Lecture Note Ser., 227, Cambridge Univ. Press, Cambridge, 1995.

55. Surgery and stratified spaces, (with Hughes) Surveys on surgery theory, Vol. 2, 319-352, Ann. of Math. Stud., 149, Princeton Univ. Press, Princeton, NJ, 2001

56. Review of "Algebraic L-theory and topological manifolds", by A.Ranicki, Bull AMS 33(1996) 93-99

57. SLn(Z) does not act on small tori, AMS/IP Stud. Adv.Math, 2.1 (1997) 406-408.

58. Microsurgery on stratified spaces, AMS/IP Studies in Advanced Mathematics, 2(1997) 509-521

59. Algorithmic aspects on homeomorphism problems (with A.Nabutovsky) Contemp Math 231 (1999) 245-250

60. Higher Rho Invariants, Contemp Math 231 (1999) 315-320

61. Large Riemannian Manifolds which are Flexible ( Ann. of Math. (2) 157 (2003), no. 3, 919-938., with Dranishnikov and Ferry)

62. Equivariant Periodicity for Abelian Group Actions (with Yan) Adv. Geom. 1 (2001) 49-70.

63. Arithmetic manifolds of positive scalar curvature(with Block) JDG 52 (1999), no. 2, 375-406.

64. Neighborhoods in stratified spaces with two strata (with Hughes, Taylor, and Williams) Topology 39 (2000) 873-919.

65. On smooth surgery II (preprint)

66. Critical points of Riemannian functionals and arithmetic groups (with A. Nabutovsky) Math Publ d'IHES, 92 (2000) 5-62.

67. Nonlinear averaging of embeddings and group actions, Contemp Math 231 (1999) 307-314.

68. The fractal geometry of Riem/Diff I (with Nabutovsky) Geometriae Dedicata 101 (2003) 1-54.

69. Surgery theoretic methods in group actions. (with Cappell) Surveys on surgery theory, Vol. 2, 285-317, Ann. of Math. Stud., 149, Princeton Univ. Press, Princeton, NJ, 2001

70. On the zero-in-the-spectrum conjecture (with M. Farber) Ann of Math 154 (2001) 139-154.

71. On invariants of Hirzebruch and Cheeger-Gromov. (with Chang) Geometry and Topology 7 (2003) 311-319.

72. The Topological Social Choice Problem, Revisited Journal of Economic Theory 115 (2005) 377-384.

73. Relative hyperbolization and aspherical bordism (with M.Davis and T.Januskiewicz.) JDG 58 (2001) 535-541.

74. Isovariant periodicity for compact group actions, (with M.Yan.) Adv. Geo 5 (2005) 363-376

75. The signature operator at 2 (with J.Rosenberg.) Topology 45 (2006) 47-63

76.The Novikov conjecture for linear groups (with E.Guentner, and N.Higson.) Math Publ. d'IHES 101 (2005) 243-268

77.On Novikov-type conjectures, (with S.S.Chang.) Clay Institute Monograph on Noncommutative Geometry, 6(2006) 43-70.

78. Hidden symmetries and arithmetic manifolds (with B. Farb) Proceedings of Robert Brooks Memorial Conference, Contemp. Math. 387, (2005) 111-119.

79. Isometries, rigidity, and universal covers, (with B. Farb) Ann of Math 168 (2008) 915-940.

80. Higher Todd classes and holomorphic group actions, (with J. Block) Pure and Applied Math Q. 2(2006) 1237-1253.

81. On the generalized Nielsen realization problem (with J. Block) Comm Math Helv 83 (2008) 21-33

82. An etale approach to the Novikov conjecture (with A.N.Dranishnikov and S.Ferry) Comm. Pure and Applied Math 61 (2008) 139-155

83. Desingularizing homology manifolds (with J.Bryant, S.Ferry, and W.Mio) Geometry and Topology 11 (2007) 1289-1314.

84. Examples of exotic stratifications (with B.Hughes, L.Taylor, and B.Williams, Geometry and Topology 11(2007) 1477-1505.

85. Homology manifolds (for the Handbook of geometric topology, R. Davermann, editor, Elsevier, to appear)

86. Topological non-rigidity of non-uniform lattices (with S.S. Chang) CPAM 60(2007) 282-290.

87. Betti numbers of finitely presented groups and very rapidly growing functions (with A.Nabutovsky) Topology 46(2007)211-223

88. Final values of functors, (Issue of L'Enseign. Math in honor of Guido Mislin)

89. E7, Wirtinger inequalities, Cayley 4-form, and Homotopy, (with V.Bangert, M.Katz, and S.Shnider) Duke Math. J. Volume 146, Number 1 (2009), 35-70.

90. Replacement theorems for compact group actions: the 2 rho theorem, (with S.Cappell and M.Yan) Pure and Applied Math Quarterly 8 (2012) 53-78.

91. Some Remarks inspired by the C^0 Zimmer program. Geometry, Rigidity, and Group Actions, University of Chicago press (2011) 262-282.

92. Finding the homology of submanifolds with high confidence from random samples, (with P.Niyogi, and S.Smale.) Combinatorial and Discrete Geometry 39 (2008) 419-441.

93. A topological view of unsupervised learning from noisy data, (with P.Niyogi and S.Smale) SIAM J. of Computing 20(2011) 646-663.

94. The intrinsic asymmetry and inhomogeneity of Teichmuller space, (with B.Farb) Duke Math. J, 155(2010) 91-103

95. Fixed point theories on noncompact manifolds Journal of Fixed Point Theory and its Applications 6(2009) 15-25.

96. Aspherical manifolds with hyperbolic fundamental group (with A.Barthels and W. Lueck) JDG 86(2010) 1-16.

97. Taming three manifolds using scalar curvature. (with S.Chang and G.Yu) Geom. Ded, 148 (2010) 3-14

98. Multiaxial U(n)-manifolds (with S.Cappell and M.Yan) to appear in JEMS

99. Persistent Homology for Random Fields and Complexess (with R.Adler, O.Bobrowski, M.Borman, and E.Sabag) IMS Collections 6 (2010) 124-143.

100. What is…Persistent Homology? Notices AMS January 2011 pp.36-39.

101. Relative Systoles of relative-essential 2-complexes (with M.Katz, S.Shnider, S.Soubarau, and K.Usadi-Katz) AGT 11(2011) 197-217.

102. Closed aspherical manifolds with center (with S.Cappell and M.Yan) Journal of Topology 6(2013) 1009-1018 .

103. The complexity of some topological inference problems. J of FOCM, 14 (2014) 1277-1285.

104. Quantitative algebraic topology and Lipschitz homotopy. (with Steve Ferry) PNAS 100 (2013) 19246-19250.

105. Modular symbols and the topological non-rigidity of arithmetic manifolds. (with Stanley Chang) CPAM, to appear

106. Crackle: The homology of noise (with Robert Adler and Omer Bobrowski) Discrete and Combinatorial Geometry, to appear

107. Finite part of K-theory for groups finitely embeddable into Hilbert Space and the degree of non-rigidity of manifolds. (with Guoliang Yu) G&T, to appear.

108. Review of “Large Scale Geometry by Nowak and Yu” Bull AMS 52 (2015) 141-150.

(with Dranishnikov and Ferry, see arxiv)

110. Additivity of higher rho invariants and nonrigidity of topological manifolds. (with Z.Xie and G.Yu, see arxiv)

111. On the vanishing of homology in Random Cech complexes. (with O. Bobrowski) Random Structures and Algorithms, to appear,

112. A fixed point theorem for periodic maps on locally symmetric manifolds, St. Petersburg Math Journal (“Algebra and Analysis”) , to appear,

113. On the stable Cannon conjecture (with S.Ferry and W.Lueck, see arxiv)

114. Positive scalar curvature and a new index theory for noncompact manifolds (with S.Chang and G.Yu)

115. Contractible manifolds with exotic positive scalar curvature behavior (with S.Chang and G.Yu) Manifolds and K-theory, 51–64, Contemp. Math., 682, Amer. Math. Soc., Providence, RI, 2017.

116. A trichotomy theorem for transformation groups of locally symmetric manifolds and topological rigidity. Adv. Math. 327 (2018), 25–46. (with S.Cappell and A.Lubotzky)

117. Quantitative nullhomotopy and rational homotopy type (with G. Chambers and F.Manin, to appear in GAFA, see arxiv)

118. Quantitative nullcobordism (with G. Chambers, D.Dotterer, and F.Manin, to appear in JAMS)

119. The Gromov-Guth-Whitney Embedding theorem (with F.Manin, Appendix to "Quantitative Nullcobordism", JAMS to appear)

120. Integral and rational mapping classes (with F.Manin, see arxiv)

121. The reach of randomly embedded manifolds (with R.Adler, S.Krishnan, and J.Taylor) Probability Theory and Related Fields (to appear)

122. Interpolation, the rudimentary geometry of Lipschitz function spaces, and geometric complexity (FOCM 2017 Barcelona talk)