Singularities, expanders and topology of maps. Part 1: Homology versus volume in the spaces of cycles

Mikhael Gromov

Research output: Contribution to journalArticle

Abstract

We find lower bounds on the topological complexity of the critical (values) sets Σ(F)⊂Y of generic smooth maps F: X→Y, as well as on the complexity of the fibers F-1 (y)⊂ X in terms of the topology of X and Y, where the relevant topological invariants of X are often encoded in the geometry of some Riemannian metric supported by X.

Original languageEnglish (US)
Pages (from-to)743-841
Number of pages99
JournalGeometric and Functional Analysis
Volume19
Issue number3
DOIs
StatePublished - 2009

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Topological Complexity
Expander
Topological Invariants
Riemannian Metric
Critical value
Homology
Fiber
Singularity
Lower bound
Topology
Cycle

Keywords

  • Expanders
  • Hyperbolic manifolds
  • Morse theory
  • Simplicial volume
  • Singularities

ASJC Scopus subject areas

  • Geometry and Topology
  • Analysis

Cite this

Singularities, expanders and topology of maps. Part 1 : Homology versus volume in the spaces of cycles. / Gromov, Mikhael.

In: Geometric and Functional Analysis, Vol. 19, No. 3, 2009, p. 743-841.

Research output: Contribution to journalArticle

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