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Abelian Gauge Theory, Knots and Odd Khovanov Homology
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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.
Forward citations
Cited by 2 Pith papers
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A module structure on odd Khovanov homology and the odd invariant for ribbon 2-knots
Reduced odd Khovanov homology is a module over Λ*H1(Σ(L)), implying n(F)=|H1(Σ(F))| for ribbon 2-knots and injectivity of ribbon concordances over Q and Z_{2^k}.
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Multi-framed real monopole Floer theory
Constructs multi-framed real monopole Floer homology for 3-manifolds with involutions and defines Z-valued invariants for 4-manifolds with involutions.
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