A Geometric Homology Representative in the Space of Long Knots

Details A Geometric Homology Representative in the Space of Long Knots A Geometric Homology Representative in the Space of Long Knots

2011-11-16

arxiv.org/abs/1111.3910v1

Mathematics

Algebraic Topology

18 pages, 10 figures

Scientific paper

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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