Frobenius Modules and Essential Surface Cobordisms
J. Scott Carter (Univ. of South Alabama), Masahico Saito (Univ. of, South Florida)
TL;DR
This paper introduces an algebraic framework using Frobenius modules to represent surface cobordisms and essential curves, unifying the algebraic understanding of categorified Jones polynomials in thickened surfaces and virtual knots.
Contribution
It presents a novel algebraic system based on Frobenius modules and comodules for modeling surface cobordisms and essential curves in thickened surfaces.
Findings
Provides a unified algebraic view of categorified Jones polynomials
Constructs explicit algebraic models for surface cobordisms
Enhances understanding of virtual knots through algebraic structures
Abstract
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic view of states of categorified Jones polynomials in thickened surfaces and virtual knots. Constructions of such system are presented.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications