, Volume 20, Issue 2, pp 416-526
Date: 30 Jul 2010

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 : 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.