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Cohomology of the toric arrangement associated with An\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_n$$\end{document}

Authors
  • Bergvall, Olof1
  • 1 Uppsala universitet, Matematiska institutionen, Uppsala, 751 06, Sweden , Uppsala (Sweden)
Type
Published Article
Journal
Journal of Fixed Point Theory and Applications
Publisher
Springer International Publishing
Publication Date
Dec 27, 2018
Volume
21
Issue
1
Identifiers
DOI: 10.1007/s11784-018-0655-x
Source
Springer Nature
Keywords
License
Green

Abstract

We compute the total cohomology of the complement of the toric arrangement associated with the root system An\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_n$$\end{document} as a representation of the corresponding Weyl group via fixed point theory of a “twisted” action of the group. We also provide several proofs of an explicit formula for the Poincaré polynomial of the complement of the toric arrangement associated with An\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_n$$\end{document}.

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