Ambidextrous homology theories

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• Jeremy Hahn (Cambridge)
• Wednesday 05 March 2025, 16:00-17:00
• CMS, MR15.

If you have a question about this talk, please contact Oscar Randal-Williams.

Given a homology theory E and an E-orientable manifold M, there exists a fundamental class in the E homology of M.  Some homology theories, including ordinary homology with rational coefficients, are “ambidextrous”—-they admit fundamental classes not only for manifolds, but also manifolds equipped with finite group actions.  I will give a brief introduction to these ambidextrous theories and then turn to some recent applications of them.  In particular, they have been applied by Abouzaid—Blumberg and Abouzaid—McLean—Smith within symplectic topology, by a number of people to the study of etale cohomology in arithmetic geometry, and to the problem of constructing continuous maps between spheres.

This talk is part of the Differential Geometry and Topology Seminar series.

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