Relative homological representations of framed mapping class groups
| Autor: | Aaron Calderon, Nick Salter |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Fundamental group General Mathematics 010102 general mathematics Geometric Topology (math.GT) Group Theory (math.GR) Homology (mathematics) 16. Peace & justice 01 natural sciences Mapping class group 010101 applied mathematics Mathematics - Geometric Topology Kernel (algebra) Monodromy FOS: Mathematics Homomorphism 0101 mathematics Abelian group Mathematics - Group Theory Orbifold Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society. 53:204-219 |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms.12412 |
| Popis: | Let $\Sigma$ be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group" on the homology of $\Sigma$ relative to its boundary (respectively marked points), describing the image as the kernel of a certain crossed homomorphism related to classical spin structures. Applying recent work of the authors, we use this to describe the monodromy action of the orbifold fundamental group of a stratum of abelian differentials on the relative periods. Comment: 18 pages. Final version, as appeared in B. Lond. Math. Soc |
| Databáze: | OpenAIRE |
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