Swan-Tate cohomology of meromorphic circle actions

2024/03/27 by Jack Morava, Morava, J · 1 citation
Mathematics · #55Nxx #57R91 #74A15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2403.19714

openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology t_\T E of a complex-oriented E_∞ ring-spectrum E is the extension of a Hopf algebra by its dual, which provides an algebraic rigidification of geometric interest. This note reviews the cases E = H,K and MU, with special attention to λ-ring structures.

Cited by

• On a complex topological orientation for circle-equivariant K-theory

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