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Discrete differential geometry in homotopy type theory

Apr 25, 2025 — Type families on higher inductive types such as pushouts can capture homotopical properties of differential geometric constructions including connections, curvature, and vector fields. We define a class of pushouts based on simplicial complexes, then …

A Supersymmetric Quantum Field Theory Formulation of the Donaldson Polynomial Invariants

Oct 1, 2002 — We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the total space …