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Diffeomorphism groups of prime 3-manifolds

  • Richard H. Bamler EMAIL logo and Bruce Kleiner
Published/Copyright: October 27, 2023

Abstract

Let X be a compact orientable non-Haken 3-manifold modeled on the Thurston geometry Nil . We show that the diffeomorphism group Diff ( X ) deformation retracts to the isometry group Isom ( X ) . Combining this with earlier work by many authors, this completes the determination the homotopy type of Diff ( X ) for any compact, orientable, prime 3-manifold X.

Award Identifier / Grant number: DMS-1906500

Award Identifier / Grant number: DMS-1711556

Award Identifier / Grant number: DMS-2005553

Funding statement: The first author was supported by NSF grant DMS-1906500. The second author was supported by NSF grants DMS-1711556, DMS-2005553, and a Simons Collaboration grant.

Acknowledgements

We thank the anonymous referee for valuable comments.

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Received: 2022-02-23
Revised: 2023-07-14
Published Online: 2023-10-27
Published in Print: 2024-01-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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