TL;DR
This paper develops a new homology theory for bikei, enhancing knot invariants for unoriented knots, links, and non-orientable surfaces in four-dimensional space.
Contribution
It introduces a modified homology and cohomology framework for bikei, enabling more effective invariants for complex knot and surface classifications.
Findings
Bikei 2-cocycles enhance counting invariants
New homology theory applicable to unoriented knots and surfaces
Improved classification tools for knotted surfaces in 4D
Abstract
We introduce a modified homology and cohomology theory for involutory biquandles (also known as \textit{bikei}). We use bikei 2-cocycles to enhance the bikei counting invariant for unoriented knots and links as well as unoriented and non-orientable knotted surfaces in .
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
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology