Homological stability and stable moduli of flat manifold bundles

Sam Nariman

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We prove that the group homology of the diffeomorphism group of #gSn×Sn\int(D2n) as a discrete group is independent of g in a range, provided that n>2. This answers the high dimensional version of a question posed by Morita about surface diffeomorphism groups made discrete. The stable homology is isomorphic to the homology of a certain infinite loop space related to the Haefliger's classifying space of foliations. One geometric consequence of this description of the stable homology is a splitting theorem that implies certain classes called generalized Mumford–Morita–Miller classes lift to a secondary R/Z-invariants for flat (#gSn×Sn)-bundles provided g≫0.

Original languageEnglish (US)
Pages (from-to)1227-1268
Number of pages42
JournalAdvances in Mathematics
Volume320
DOIs
StatePublished - Nov 7 2017

Keywords

  • Diffeomorphism groups
  • Flat bundles
  • Godbillon–Vey invariants
  • Haefliger classifying space
  • Homological stability
  • Infinite loop space

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Homological stability and stable moduli of flat manifold bundles'. Together they form a unique fingerprint.

Cite this