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Mapping class groups of
covers with boundary and braid group embeddings
Tyrone Ghaswala and Alan McLeay |
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Algebraic & Geometric Topology 20 (2020) 239–278
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Abstract |
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We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides with the entire mapping class group of the surface. As a consequence, we construct infinite families of nongeometric embeddings of the braid group into mapping class groups in the sense of Wajnryb. Indeed, our embeddings map standard braid generators to products of Dehn twists about curves forming chains of arbitrary length. As key tools, we use the Birman–Hilden theorem and the action of the mapping class group on a particular fundamental groupoid of the surface. |
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Keywords
mapping class groups, braid groups, covering spaces
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Mathematical Subject Classification 2010
Primary: 57M12
Secondary: 20F36, 20L05
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References |
Publication
Received: 11 May 2018
Revised: 11 March 2019
Accepted: 1 April 2019
Published: 23 February 2020
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Authors |
| Tyrone Ghaswala | |
| Department of Mathematics University of Manitoba Winnipeg, MB Canada |
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| Alan McLeay | |
| Mathematics Research Unit University of Luxembourg Esch-sur-Alzette Luxembourg |
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