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Finite groups acting on homology manifolds

Aschbacher, Michael (1997) Finite groups acting on homology manifolds. Pacific Journal of Mathematics, 181 (3). pp. 3-36. ISSN 0030-8730.

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In this paper we study homology manifolds T admitting the action of a finite group preserving the structure of a regular CW-complex on T. The CW-complex is parameterized by a poset and the topological properties of the manifold are translated into a combinatorial setting via the poset. We concentrate on n-manifolds which admit a fairly rigid group of automorphisms transitive on the n-cells of the complex. This allows us to make yet another translation from a combinatorial into a group theoretic setting. We close by using our machinery to construct representations on manifolds of the Monster, the largest sporadic group. Some of these manifolds are of dimension 24, and hence candidates for examples to Hirzebruch's Prize Question in [HBJ], but unfortunately closer inspection shows the A^-genus of these manifolds is 0 rather than 1, so none is a Hirzebruch manifold.

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Additional Information:Pacific journal of mathematics, Vol. 181, No. 3, 1997 - Dedicated to the Memory of Olga Taussky-Todd. This work was partially supported by NSF DMS-9101237 and NSF DMS-9622843.
Issue or Number:3
Record Number:CaltechAUTHORS:ASCpjm97
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:544
Deposited By: Archive Administrator
Deposited On:14 Jul 2005
Last Modified:02 Oct 2019 22:34

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