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

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Abstract

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

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  1. IHES, 35 route de Chartres, Bures sur Yvette, 91440, France

    Mikhail Gromov

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, NewYork, NY, 10012, USA

    Mikhail Gromov

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Gromov, M. Singularities, Expanders and Topology of Maps. Part 2: from Combinatorics to Topology Via Algebraic Isoperimetry. Geom. Funct. Anal. 20, 416–526 (2010). https://doi.org/10.1007/s00039-010-0073-8

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