On Algebraic Structures Implicit in Topological Quantum Field Theories
L. Crane, D. Yetter
TL;DR
This paper reveals that well-behaved 3D and 4D topological quantum field theories inherently include specific algebraic structures such as Hopf categories and trialgebras, highlighting deep mathematical connections.
Contribution
It demonstrates the presence of algebraic structures like Hopf categories and trialgebras in 3D and 4D TQFTs, advancing understanding of their mathematical foundations.
Findings
Identification of Hopf categories in 4D TQFTs
Discovery of trialgebras in 4D TQFTs
Establishment of algebraic structures in well-behaved 3D and 4D TQFTs
Abstract
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Operator Algebra Research