Geodesic
Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence
Laurent Bartholdi1 orcid ; Dzmitry Dudko2
1Universität des Saarlandes, Saarbrücken, Germany
2Stony Brook University, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1197-1265

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DOI

Let f~​:(S2,A)↺ be a Thurston map and let M(f~​) be its mapping class biset: isotopy classes rel A of maps obtained by pre- and post-composing f~​ by the mapping class group of (S2,A). Let A⊆A be an f~​-invariant subset, and let f:(S2,A)↺ be the induced map. We give an analogue of the Birman short exact sequence: just as the mapping class group Mod(S2,A) is an iterated extension of Mod(S2,A) by fundamental groups of punctured spheres, M(f~​) is an iterated extension of M(f) by the dynamical biset of f.
DOI : 10.4171/ggd/629
Classification : 57-XX, 20-XX, 37-XX
Mots-clés : Thurston maps, mapping class group, mapping class biset, erasing punctures, Birman exact sequence

Laurent Bartholdi  1   ; Dzmitry Dudko  2

1 Universität des Saarlandes, Saarbrücken, Germany
2 Stony Brook University, USA 
Laurent Bartholdi; Dzmitry Dudko. Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence. Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1197-1265. doi: 10.4171/ggd/629
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     author = {Laurent Bartholdi and Dzmitry Dudko},
     title = {Algorithmic aspects of branched coverings {III/V.} {Erasing} maps, orbispaces, and the {Birman} exact sequence},
     journal = {Groups, geometry, and dynamics},
     pages = {1197--1265},
     year = {2021},
     volume = {15},
     number = {4},
     doi = {10.4171/ggd/629},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/629/}
}
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