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

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. © 2010 Springer Basel AG.