arXiv 1402.02802014-02math.GTmath.AT

Topological rigidity and actions on contractible manifolds with discrete singular set

Frank Connolly, James F. Davis, Qayum Khan

备注：: 21 pages, slightly modified title, added a last section for examples
发表信息：: Transactions of the American Mathematical Society, Series B, Volume 2 (2015), 113-133
DOI：: 10.1090/btran/9

英文摘要：

The problem of equivariant rigidity is the $Γ$-homeomorphism classification of $Γ$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $Γ$. In other words, this is the classification of cocompact $E_{fin}Γ$-manifolds. We use surgery theory, algebraic $K$-theory, and the Farrell--Jones Conjecture to give this classification for a family of groups which satisfy the property that the normalizers of nontrivial finite subgroups are themselves finite. More generally, we study cocompact proper actions of these groups on contractible manifolds and prove that the $E_{fin}$-condition is always satisfied.

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