Novikov homology and noncommutative Alexander polynomials

Stefan Friedl

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arXiv · 1606.03587

Novikov homology and noncommutative Alexander polynomials

Stefan Friedl

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Abstract

In the early 2000's Cochran and Harvey introduced non-commutative Alexander polynomials for 3-manifolds. Their degrees give strong lower bounds on the Thurston norm. In this paper we make the case that the vanishing of a certain Novikov-Sikorav homology module is the correct notion of a monic non-commutative Alexander polynomial. Furthermore we will use the opportunity to give new proofs of several statements about Novikov-Sikorav homology in the three-dimensional context.

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Stefan Friedl. 2016-06-11. Novikov homology and noncommutative Alexander polynomials. https://arxiv.org/abs/1606.03587

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