Families of diffeomorphisms and concordances detected by trivalent graphs

Author:

Botvinnik Boris1,Watanabe Tadayuki2

Affiliation:

1. Department of Mathematics University of Oregon Eugene Oregon USA

2. Department of Mathematics Kyoto University Kyoto Japan

Abstract

AbstractWe study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non‐trivial elements in homotopy groups are lifted to homotopy groups of the moduli space of ‐cobordisms . As a geometrical application, we show that those elements in for are also lifted to the rational homotopy groups of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups of moduli space of concordances of positive scalar curvature metrics on with fixed‐round metric on the boundary .

Funder

Simons Foundation

Japan Society for the Promotion of Science

Research Institute for Mathematical Sciences

Kyoto University

Publisher

Wiley

Subject

Geometry and Topology

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