Involution on pseudoisotopy spaces and the space of nonnegatively curved metrics

Autor:	Bustamante, Mauricio, Farrell, Francis Thomas, Jiang, Yi
Rok vydání:	2017
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology Mathematics - Differential Geometry Mathematics - K-Theory and Homology 57R50 55N91 19D10
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages, to appear in Transactions of the AMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.07529 Zobrazit plný text záznamu View this record from Arxiv