Foams, iterated wreath products, field extensions and Sylvester sums

2021/07/16 by Mee Seong Im, Mikhail Khovanov, Im, Mee Seong +1
Mathematics · #13P15 #18M30 #20C99 #20E22 #57K99 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary: 57K16 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary: 18N25

paper · pdf · doi:10.48550/arxiv.2107.07845

openalex publication_date 2021/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Certain foams and relations on them are introduced to interpret functors and natural transformations in categories of representations of iterated wreath products of cyclic groups of order two. We also explain how patched surfaces with defect circles and foams relate to separable field extensions and Galois theory and explore a relation between overlapping foams and Sylvester double sums. In the appendix, joint with Lev Rozansky, we compare traces in two-dimensional TQFTs coming from matrix factorizations with those in field extensions.

Citations

• The \mathfraksl_n foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Annular Evaluation and Link Homology
• Universal construction of topological theories in two dimensions

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