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

Mikhael Gromov

Research output: Contribution to journalArticle

Abstract

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
Volume20
Issue number2
DOIs
StatePublished - 2010

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Isoperimetry
Algebraic topology
Expander
Continuous Map
Combinatorics
Polyhedron
Cohomology
Fiber
Singularity
Lower bound
Topology
Algebra
Invariant

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology
  • Analysis

Cite this

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

In: Geometric and Functional Analysis, Vol. 20, No. 2, 2010, p. 416-526.

Research output: Contribution to journalArticle

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