Diffeomorphism groups of prime 3-manifolds

Richard H. Bamler, Bruce Kleiner

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)23-35
Number of pages13
JournalJournal fur die Reine und Angewandte Mathematik
Issue number806
StatePublished - Jan 1 2024

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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