CaltechAUTHORS
  A Caltech Library Service

The spherical Plateau problem for group homology

Song, Antoine (2022) The spherical Plateau problem for group homology. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20221026-538906000.1

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20221026-538906000.1

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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2202.10636DOIDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
Clay Mathematics InstituteUNSPECIFIED
DOI:10.48550/arXiv.2202.10636
Record Number:CaltechAUTHORS:20221026-538906000.1
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20221026-538906000.1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117590
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:28 Oct 2022 15:34
Last Modified:28 Oct 2022 15:34

Repository Staff Only: item control page