Published October 28, 2022
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The spherical Plateau problem for group homology
- Creators
- Song, Antoine
Abstract
Given a group homology class h of a countable group Γ, we study a corresponding homological Plateau problem inside a canonical classifying space of Γ, which is defined using the regular representation of Γ and which is locally isometric to a Hilbert unit sphere. We investigate the relation between group theoretic properties of the pair (Γ,h) and the geometry of its Plateau solutions. For instance, we prove that for a closed oriented 3-manifold M, the intrinsic geometry of any Plateau solution is given by the hyperbolic part of M endowed with one third of its hyperbolic metric.
Additional Information
I am grateful to Gérard Besson, Gilles Courtois, John Lott, Ian Agol, Richard Bamler, Song Sun, Jason Manning, Stéphane Sabourau, Camillo De Lellis, Xin Zhou, Alexander Nabutovsky, Shi Wang, Ben Lowe for many insightful and stimulating discussions during the writing of this article. This research was conducted during the period A.S. served as a Clay Research Fellow.Additional details
- Eprint ID
- 117590
- Resolver ID
- CaltechAUTHORS:20221026-538906000.1
- Clay Mathematics Institute
- Created
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2022-10-28Created from EPrint's datestamp field
- Updated
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2022-10-28Created from EPrint's last_modified field