A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Modified bikei homology enhances knot and surface invariants.
Algorithm finds finite fundamental bikei for virtual knots.
Enhanced bikei modules distinguish unoriented and non-orientable surface-links.
We identify a subcategory of biracks which define counting invariants of unoriented links, which we call involutory biracks. In particular, involutory biracks of birack rank N=1 are biquandles, which we call bikei. We define counting invariants of unoriented classical and virtual links using finite involutory biracks, …
Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in ; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are defined only for marked vertex diagrams representing knotted orientable surfaces; we e…