2010/01/05 by J. Scott Carter, Carter, J. Scott, Masahico Saito +1 · 1 citation
Mathematics · #16T10 #17B37 #57M25 #81R50 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:16T10 #msc:17B37 #msc:57M25 #msc:81R50
paper · pdf · doi:10.48550/arxiv.1001.0775
11 pages; 14 figures
arxiv created 2010/01/05 · openalex publication_date 2010/01/05 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of commutative Frobenius algebras, where saddle points correspond to multiplication and comultiplication. In this paper, we explore algebraic operations that branch lines derive under TQFT. In particular, we investigate Lie bracket and bialgebra structures. Relations to the original Frobenius algebra structures are discussed both algebraically and diagrammatically.