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math.GT2025
An Extension of Khovanov Homology to Immersed Surface Cobordisms
Scott Carter, Benjamin Cooper, Mikhail Khovanov +1
We show that an oriented surface in containing double point singularities induces a map between the Khovanov homology groups of its boundary links in a functorial wa…
math.GT2025
Trisected Rainbows and Braids
Román Aranda, Scott Carter, Julia Courtney +1
New explicit procedures for passing among triplane diagrams, braid movies, and braid charts for knotted surfaces in are presented. To this end, rainbow diagrams, whi…
math.GT2015★ 21 cited
Homology for Quandles with Partial Group Operations
J. Scott Carter, Atsushi Ishii, Masahico Saito +1
A quandle is a set that has a binary operation satisfying three conditions corresponding to the Reidemeister moves. Homology theories of quandles have been developed in a way simil…