Twisted skein homology
Nguyen D. Duong, Lawrence P. Roberts
TL;DR
This paper extends twisted Khovanov homology techniques to links and tangles in surface bundles, providing a new invariant chain complex and insights into elta-graded homology for alternating links.
Contribution
It introduces a novel invariant chain complex based on non-contractible circles, enhancing understanding of surface-based link homologies.
Findings
Describes an invariant chain complex for links in surface bundles.
Provides analysis of elta-graded homology for alternating links.
Connects twisted Khovanov homology with surface link invariants.
Abstract
We apply the techniques of totally twisted Khovanov homology to the constructions by M. Asaeda, J. Przytycki, and A. Sikora of Khovanov type homologies for links and tangles in I-bundles over (orientable) surfaces. As a result we describe an invariant chain complex built out of resolutions with only non-contractible circles. We use these to understand the \delta-graded homology for links with alternating projection to the surface.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis