Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry

Mikhail Gromov

Research output: Contribution to journalArticle


We find lower bounds on the topology of the fibers of continuous maps F: X → Y in terms of combinatorial invariants of certain polyhedra and/or of the cohomology algebras H*(X). Our exposition is conceptually related to but essentially independent of Part 1 of the paper.

Original languageEnglish (US)
Pages (from-to)416-526
Number of pages111
JournalGeometric and Functional Analysis
Issue number2
StatePublished - Jul 29 2010



  • Expanders
  • Isoperimetric inequalities
  • Semisimplicial complexes
  • Spaces of cycles

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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