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The homotopy type of
elliptic arrangements
Emanuele Delucchi and Roberto Pagaria |
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Algebraic & Geometric Topology 21 (2021) 2037–2063
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Abstract |
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We give combinatorial models for the homotopy type of complements of elliptic arrangements, ie 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. |
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Keywords
elliptic arrangements, Salvetti complexes, polyhedral
complexes, CW complexes, acyclic categories, braid group,
configuration spaces
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Mathematical Subject Classification 2010
Primary: 55U05
Secondary: 05E45, 20F36, 55R80
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References |
Publication
Received: 18 March 2020
Revised: 23 June 2020
Accepted: 9 July 2020
Published: 18 August 2021
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Authors |
| Emanuele Delucchi | |
| University of Applied Arts and
Sciences of Southern Switzerland Lugano Switzerland |
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| http://www.maestran.ch/math/ | |
| Roberto Pagaria | |
| Dipartimento di Matematica Università di Bologna Bologna Italy |
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| https://www.dm.unibo.it/~roberto.pagaria/ | |
