The homotopy type of elliptic arrangements

Abstract

We give combinatorial models for the homotopy type of complements of elliptic arrangements (i.e., certain sets of abelian subvarieties in a product of elliptic curves). We give a presentation of the fundamental group of such spaces and, as an application, we treat the case of ordered configuration spaces of elliptic curves. Our models are finite polyhedral CW complexes, and our combinatorial tools of choice are acyclic categories (small categories without loops). As a stepping stone, we give a characterization of which acyclic categories arise as face categories of polyhedral CW complexes.

minor changes, to appear in Algebr. Geom. Topol

References in corpus (5)

• Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements
• Two Examples of Toric Arrangements
• Cohomology rings of compactifications of toric arrangements
• Combinatorics of Toric Arrangements
• Poincaré polynomial of elliptic arrangements is not a specialization of the Tutte polynomial