Detecting torsion in skein modules using Hochschild homology

Michael McLendon

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Detecting torsion in skein modules using Hochschild homology

Michael McLendon

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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.

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Michael McLendon. 2004-05-20. Detecting torsion in skein modules using Hochschild homology. https://arxiv.org/abs/math/0405395

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