Duality pairings with the analytic structure group

2025/06/16 by Wulff, Christopher, Rudolf Zeidler, Zeidler, Rudolf
Mathematics · Physics and Astronomy · #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematics and Applications #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2506.13703

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We construct a slant product S^{G× H}_p(X× Y)⊗ K_-q(\mathfrakc^red Y\rtimes H)→ K_p-q(C^∗_G X) on the analytic structure group of Higson and Roe and the K-theory of the stable Higson compactification taking values in the (equivariant) Roe algebra. This complements the slant products constructed in earlier work of Engel and the authors ( arXiv:1909.03777 [math.KT] ). The distinguishing feature of our new slant product is that it specializes to a duality pairing S^H_p(Y) ⊗ K_-p(\mathfrakc^red (Y)\rtimes H)→ ℤ which can be used to extract numerical invariants out of elements in the analytic structure group such as rho-invariants associated to positive scalar curvature metrics.

Citations

• Mapping analytic surgery to homology, higher rho numbers and metrics of positive scalar curvature
• Additivity of higher rho invariants and nonrigidity of topological manifolds
• Coarse co-assembly as a ring homomorphism
• Positive scalar curvature, higher rho invariants and localization algebras

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• Mapping analytic surgery to homology, higher rho numbers and metrics of positive scalar curvature
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