The sl(2) foam cohomology via a TQFT
Carmen Caprau
TL;DR
This paper develops a new cohomology theory for oriented links using a specialized TQFT, providing a categorification of the quantum sl(2) invariant through foam cobordisms.
Contribution
It introduces a universal dot-free sl(2) foam cohomology for links constructed via a TQFT, advancing the categorification of quantum invariants.
Findings
Constructed a cohomology theory for links using singular cobordisms.
Provided a TQFT-based description of the universal dot-free sl(2) foam cohomology.
Categorified the quantum sl(2) invariant for links.
Abstract
We construct a cohomology theory for oriented links using singular cobordisms and a special type of 2-dimensional Topological Quantum Field Theory (TQFT), categorifying the quantum sl(2) invariant. In particular, we give a description of the universal dot-free sl(2) foam cohomology for links via a TQFT.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics