Can I read Involution on Pseudoisotopy Spaces and the Space of Nonnegatively Curved Metrics on EtoBox?

Involution on Pseudoisotopy Spaces and the Space of Nonnegatively Curved Metrics by Bustamante, Mauricio; Farrell, Francis Thomas; Jiang, Yi is a scholarly article available to read on EtoBox.

What is Involution on Pseudoisotopy Spaces and the Space of Nonnegatively Curved Metrics about?

We prove that certain involutions defined by Vogell and Burghelea-Fiedorowicz on the rational algebraic $K$-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 group of the free loop space of a simply-connected manifold. As an application, we give explicit dimensions of the open manifolds $V$ that appear in Belegradek-Farrell-Kapovitch's work for which the spaces of complete nonnegatively curved metrics on $V$ have nontrivial rational homotopy groups.

Author

Bustamante, Mauricio; Farrell, Francis Thomas; Jiang, Yi

Published

2017

Language

EN