Representations of the homotopy surface category of a simply connected space

1999/10/05 by M. Brightwell, Mark Brightwell, Paul Turner +3
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA

paper · pdf · doi:10.48550/arxiv.math/9910026

9 pages, 2 figures

arxiv created 1999/10/05 · openalex publication_date 1999/10/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the homotopy surface category of a space which generalizes the 1+1-dimensional cobordism category of circles and surfaces to the situation where one introduces a background space. We explain how for a simply connected background space, monoidal functors from this category to vector spaces can be interpreted in terms of Frobenius algebras with additional structure.

Related

• On the homotopy type of certain cobordism categories of surfaces
• The homotopy type of the Poincaré cobordism category for surfaces
• The surface category and tropical curves
• Algebraic Presentation of 4-Dimensional 2-Handlebodies and 3-Dimensional Cobordisms
• Geometric Cobordism Categories