Special Issue for Tim Cochran; Guest Editors: J. E. Grigsby, S. Harvey, K. Orr and D. RubermanNo Access

Novikov homology and non-commutative Alexander polynomials

Stefan Friedl

Fakultät für Mathematik, Universität Regensburg, Germany

https://doi.org/10.1142/S0218216517400132Cited by:5 (Source: Crossref)

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.

In Memory of Tim Cochran

Keywords:

AMSC: 57M25, 57M27

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