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arXiv · 1111.3910

A Geometric Homology Representative in the Space of Long Knots

Kristine E. Pelatt
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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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Kristine E. Pelatt. 2011-11-16. A Geometric Homology Representative in the Space of Long Knots. https://arxiv.org/abs/1111.3910

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