2025/01/17 by Paul Großkopf, Großkopf, Paul
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2501.10113
openalex publication_date 2025/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Homotopy Quantum Field Theories as variants of Topological Quantum Field Theories are described by functors from some cobordism category, enriched with homotopical data, to a symmetric monoidal category V. A new notion of HQFTs is introduced using target pairs of spaces (X,Y) acounting for basepoints being sent to points in Y. Such (X,Y)-HQFTs are classified in dimension 1 by dualizable representations of G:=Π1(X,Y), the relative fundamental groupoid. For dimension 2, the notion of crossed loop Frobenius (G,V)-categories is introduced, generalizing crossed Frobenius G-algebras, where G is only a group. After stating generalities of these multi-object generalizations, a classification theorem of 2-dimensional (X,Y)-HQFTs via crossed loop Frobenius (G,V)-categories is proven.