Involution on pseudoisotopy spaces and the space of nonnegatively curved metrics

Bustamante, Mauricio; Farrell, Francis; Jiang, Yi

doi:10.1090/tran/8135

Involution on pseudoisotopy spaces and the space of nonnegatively curved metrics

Authors: Mauricio Bustamante, Francis Thomas Farrell and Yi Jiang
Journal: Trans. Amer. Math. Soc. 373 (2020), 7225-7252
MSC (2010): Primary 19D10; Secondary 55N91
DOI: https://doi.org/10.1090/tran/8135
Published electronically: July 28, 2020
MathSciNet review: 4155206
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Abstract: We prove that certain involutions defined by Vogell and Burghelea-Fiedorowicz on the rational algebraic -theory of spaces coincide. This gives a way to compute the positive and negative eigenspaces of the involution on rational homotopy groups of pseudoisotopy spaces from the involution on rational $S^{1}$ -equivariant homology groups of the free loop space of a simply-connected manifold. As an application, we give explicit dimensions of the open manifolds that appear in Belegradek-Farrell-Kapovitch's work for which the spaces of complete nonnegatively curved metrics on have nontrivial rational homotopy groups.

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