Gauge Theory & Characteristic Classes

← Back to Domain-Specific Families

Abstractions about curvature and characteristic classes in gauge theory, including Chern-Weil and Chern-Simons constructions, Yang-Mills flow, and their higher-categorical generalizations to infinity-bundles.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Chern–Weil homomorphism — The map sending invariant polynomials on a Lie algebra to de Rham cohomology classes represented by curvature forms of principal-bundle connections.
• Weitzenböck identity — An identity expressing one Laplace-type operator as a rough Laplacian plus a curvature-dependent lower-order term.
• Yang–Mills flow — The negative gradient flow of the Yang–Mills energy on connections, evolving curvature toward Yang–Mills critical connections.
• ∞-Chern–Simons theory — A higher-categorical generalization of Chern–Simons gauge theory formulated with higher bundles, connections and characteristic maps in a cohesive infinity-topos.
• ∞-Chern–Weil theory — A higher-geometric extension of Chern–Weil theory that constructs differential characteristic classes and cocycles for higher principal bundles and infinity-groupoids.