A Geometric Homology Representative in the Space of Long Knots
Algebraic Topology
2011-11-17 v1
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.
Keywords
Cite
@article{arxiv.1111.3910,
title = {A Geometric Homology Representative in the Space of Long Knots},
author = {Kristine E. Pelatt},
journal= {arXiv preprint arXiv:1111.3910},
year = {2011}
}
Comments
18 pages, 10 figures