Fusion 2-categories and a state-sum invariant for 4-manifolds
Christopher L. Douglas, David J. Reutter
TL;DR
This paper introduces fusion 2-categories and constructs a state-sum invariant for oriented 4-manifolds, advancing the mathematical framework for topological quantum field theories in four dimensions.
Contribution
It defines fusion 2-categories and develops a new state-sum invariant for 4-manifolds based on spherical fusion 2-categories.
Findings
Defined semisimple, fusion, and spherical fusion 2-categories
Constructed a state-sum invariant for 4-manifolds
Provided a new mathematical tool for 4D topological quantum field theories
Abstract
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology