Strings, fermions and the topology of curves on annuli
Geometric Topology
2014-11-07 v2 Algebraic Topology
Symplectic Geometry
Abstract
In previous work with Schoenfeld, we considered a string-type chain complex of curves on surfaces, with differential given by resolving crossings, and computed the homology of this complex for discs. In this paper we consider the corresponding "string homology" of annuli. We find this homology has a rich algebraic structure which can be described, in various senses, as fermionic. While for discs we found an isomorphism between string homology and the sutured Floer homology of a related 3-manifold, in the case of annuli we find the relationship is more complex, with string homology containing further higher-order structure.
Keywords
Cite
@article{arxiv.1410.2141,
title = {Strings, fermions and the topology of curves on annuli},
author = {Daniel V. Mathews},
journal= {arXiv preprint arXiv:1410.2141},
year = {2014}
}
Comments
55 pages, 9 figures. v2: further introductory details added, typos corrected