English

Detecting torsion in skein modules using Hochschild homology

Geometric Topology 2014-11-18 v1 Algebraic Topology

Abstract

Given a Heegaard splitting of a closed 3-manifold, the skein modules of the two handlebodies are modules over the skein algebra of their common boundary surface. The zeroth Hochschild homology of the skein algebra of a surface with coefficients in the tensor product of the skein modules of two handlebodies is interpreted as the skein module of the 3-manifold obtained by gluing the two handlebodies together along this surface. A spectral sequence associated to the Hochschild complex is constructed and conditions are given for the existence of algebraic torsion in the skein module of this 3-manifold.

Keywords

Cite

@article{arxiv.math/0405395,
  title  = {Detecting torsion in skein modules using Hochschild homology},
  author = {Michael McLendon},
  journal= {arXiv preprint arXiv:math/0405395},
  year   = {2014}
}

Comments

20 pages, 8 figures, uses amssymb, epsfig, amsthm packages

R2 v1 2026-07-22T17:05:42.662Z