University of Chicago
Department of Mathematics

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4:30 pm Tuesday, May 13, 2003

Algebraic Topology

Proper actions of automorphism groups of free products

Craig Jensen

If $G$ is a free product of finite groups, let $\Sigma Aut_1(G)$ denote all (necessarily symmetric) automorphisms of $G$ that do not permute factors in the free product. We show that a McCullough-Miller [D. McCullough and A. Miller, {\em Symmetric Automorphisms of Free Products}, Mem. Amer. Math. Soc. 122 (1996), no. 582] and Guti\'{e}rrez-Krsti\'{c} [M. Guti\'{e}rrez and S. Krsti\'{c}, {\em Normal forms for the group of basis-conjugating automorphisms of a free group}, International Journal of Algebra and Computation 8 (1998) 631-669] derived (also see Bogley- Krsti\'{c} [W. Bogley and S. Krsti\'{c}, {\em String groups and other subgroups of $Aut(F_n)$}, preprint] space of pointed trees is an $\underline{E} \Sigma Aut_1(G)$-space for these groups. (Joint with H. Glover and Y. Chen.)

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University of ChicagoDepartment of Mathematics

University of Chicago
Department of Mathematics