Geometric and Functional Analysis

, Volume 20, Issue 2, pp 416–526

Singularities, Expanders and Topology of Maps. Part 2: from Combinatorics to Topology Via Algebraic Isoperimetry


DOI: 10.1007/s00039-010-0073-8

Cite this article as:
Gromov, M. Geom. Funct. Anal. (2010) 20: 416. doi:10.1007/s00039-010-0073-8


We find lower bounds on the topology of the fibers \({F^{-1}(y)\subset X}\) of continuous maps F : XY 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.

Keywords and phrases

Expanders isoperimetric inequalities semisimplicial complexes spaces of cycles 

2010 Mathematics Subject Classification

05C10 05C80 06F05 53C23 05D05 55U10 

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.IHESBures sur YvetteFrance
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNewYorkUSA

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