Universal cocycle Invariants for singular knots and links

FARINATI MARCO, GARCIA GALOFRE JULIANA.

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2022

0218-2165

Given a biquandle (X,S), a function τ with certain compatibility and a pair of non commutative cocyles f,h:X×X→G with values in a non necessarily commutative group G, we give an invariant for singular knots / links. Given (X,S,τ), we also define a universal group U^{fh}_{nc}(X) and universal functions governing all 2-cocycles in X, and exhibit examples of computations. When the target group is abelian, a notion of abelian cocycle pair is given and the "state sum" is defined for singular knots/links. Computations generalizing linking number for singular knots are given. As for virtual knots, a "self-linking number" may be defined for singular knots.