2005/09/22 by Edmundo Castillo, Castillo, Edmundo, Rafael Díaz +2
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #math-ph #math.AT #math.KT #math.MP
paper · pdf · doi:10.48550/arxiv.math/0509532
18 figures
openalex publication_date 2005/09/22 · arxiv created 2008/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal d-algebra. We construct a structure of transversal 1-category on the space of chains of maps from a suspension space S(Y), with certain boundary restrictions, into a fixed compact oriented manifold. We define homological quantum field theories \HL and construct several examples of such structures. Our definition is based on the notions of string topology of Chas and Sullivan, and homotopy quantum field theories of Turaev.