Volume of representations and mapping degree

Pierre Derbez, Yi Liu, Hongbin Sun, Shicheng Wang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Given a connected real Lie group and a contractible homogeneous proper G–space X furnished with a G–invariant volume form, a real valued volume can be assigned to any representation ρ:π 1 (M)→G for any oriented closed smooth manifold M of the same dimension as X. Suppose that G contains a closed and cocompact semisimple subgroup, it is shown in this paper that the set of volumes is finite for any given M. From a perspective of model geometries, examples are investigated and applications with mapping degrees are discussed.

Original languageEnglish (US)
Pages (from-to)570-613
Number of pages44
JournalAdvances in Mathematics
StatePublished - Jul 31 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Cocompact
  • Representation volume
  • Semisimple Lie group


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