Abelian Gauge Theory, Knots and Odd Khovanov Homology

2015/08/31 by Aliakbar Daemi, Daemi, Aliakbar · 1 citation
Mathematics · #57M27 (Primary) 53C07 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:53C07 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1508.07650

78 pages

arxiv created 2015/08/31 · arxiv updated 2015/09/01

Abstract

A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to the families of 4-dimensional cobordisms. This construction and its functoriality are used to define several link invariants. The strongest version of these invariants has the form of a filtered chain complex that can recover Khovanov homology of the mirror image as a bi-graded group.

Cited by

• Cobordism maps in Khovanov homology and singular instanton homology I

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• Khovanov homology theories and their applications