A Geometric Homology Representative in the Space of Long Knots

2011/11/16 by Pelatt, Kristine E.
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.3910

Abstract

We produce explicit geometric representatives of nontrivial homology classes in the space of long knots in R^d, when d is even. We generalize results of Cattaneo, Cotta-Ramusino and Longoni to define cycles which live off of the vanishing line of a homology spectral sequence due to Sinha. We use configuration space integrals to show our classes pair nontrivially with cohomology classes due to Longoni.

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