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Thematische Bibliographien / Mapping class subgroups

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Zeitschriftenartikel

Auswahl der wissenschaftlichen Literatur zum Thema „Mapping class subgroups“

Autor: Grafiati

Veröffentlicht am 9. November 2024

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Zeitschriftenartikel zum Thema "Mapping class subgroups"

1

Matsuzaki, Katsuhiko. "Polycyclic quasiconformal mapping class subgroups." Pacific Journal of Mathematics 251, no. 2 (2011): 361–74. http://dx.doi.org/10.2140/pjm.2011.251.361.

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2

Clay, Matt, Johanna Mangahas, and Dan Margalit. "Right-angled Artin groups as normal subgroups of mapping class groups." Compositio Mathematica 157, no. 8 (2021): 1807–52. http://dx.doi.org/10.1112/s0010437x21007417.

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We construct the first examples of normal subgroups of mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non-free right-angled Artin subgroups of other groups, such as braid groups and pure braid groups, as well as many subgroups of the mapping class group, such as the Torelli subgroup. Our work recovers and generalizes the seminal result of Dahmani–Guirardel–Osin, which gives free, purely pseudo-Anosov normal subgroups of mapping class groups. We give two applications of our methods: (1) we produce an explicit proper normal subgroup of the mapping class group that is not contained in any level $m$ congruence subgroup and (2) we produce an explicit example of a pseudo-Anosov mapping class with the property that all of its even powers have free normal closure and its odd powers normally generate the entire mapping class group. The technical theorem at the heart of our work is a new version of the windmill apparatus of Dahmani–Guirardel–Osin, which is tailored to the setting of group actions on the projection complexes of Bestvina–Bromberg–Fujiwara.

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3

Calegari, Danny, and Lvzhou Chen. "Normal subgroups of big mapping class groups." Transactions of the American Mathematical Society, Series B 9, no. 30 (2022): 957–76. http://dx.doi.org/10.1090/btran/108.

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Let S S be a surface and let Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) be the mapping class group of S S permuting a Cantor subset K ⊂ S K \subset S . We prove two structure theorems for normal subgroups of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) . (Purity:) if S S has finite type, every normal subgroup of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) either contains the kernel of the forgetful map to the mapping class group of S S , or it is ‘pure’ — i.e. it fixes the Cantor set pointwise. (Inertia:) for any n n element subset Q Q of the Cantor set, there is a forgetful map from the pure subgroup PMod ⁡ ( S , K ) \operatorname {PMod}(S,K) of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) to the mapping class group of ( S , Q ) (S,Q) fixing Q Q pointwise. If N N is a normal subgroup of Mod ⁡ ( S , K ) \operatorname {Mod}(S,K) contained in PMod ⁡ ( S , K ) \operatorname {PMod}(S,K) , its image N Q N_Q is likewise normal. We characterize exactly which finite-type normal subgroups N Q N_Q arise this way. Several applications and numerous examples are also given.

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4

Kim, Heejoung. "Stable subgroups and Morse subgroups in mapping class groups." International Journal of Algebra and Computation 29, no. 05 (2019): 893–903. http://dx.doi.org/10.1142/s0218196719500346.

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For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, namely a stable subgroup and a Morse or strongly quasiconvex subgroup. Durham and Taylor [M. Durham and S. Taylor, Convex cocompactness and stability in mapping class groups, Algebr. Geom. Topol. 15(5) (2015) 2839–2859] defined stability and proved stability is equivalent to convex cocompactness in mapping class groups. Another natural generalization of quasiconvexity is given by the notion of a Morse or strongly quasiconvex subgroup of a finitely generated group, studied recently by Tran [H. Tran, On strongly quasiconvex subgroups, To Appear in Geom. Topol., preprint (2017), arXiv:1707.05581 ] and Genevois [A. Genevois, Hyperbolicities in CAT (0) cube complexes, preprint (2017), arXiv:1709.08843 ]. In general, a subgroup is stable if and only if the subgroup is Morse and hyperbolic. In this paper, we prove that two properties of being Morse and stable coincide for a subgroup of infinite index in the mapping class group of an oriented, connected, finite type surface with negative Euler characteristic.

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5

Leininger, Christopher J., and D. B. McReynolds. "Separable subgroups of mapping class groups." Topology and its Applications 154, no. 1 (2007): 1–10. http://dx.doi.org/10.1016/j.topol.2006.03.013.

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6

Bavard, Juliette, Spencer Dowdall, and Kasra Rafi. "Isomorphisms Between Big Mapping Class Groups." International Mathematics Research Notices 2020, no. 10 (2018): 3084–99. http://dx.doi.org/10.1093/imrn/rny093.

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Abstract We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these “big” mapping class groups and shows that each finite-index subgroup has finite outer automorphism group. As a key ingredient, we prove that all simplicial automorphisms between curve complexes of infinite-type orientable surfaces are induced by homeomorphisms.

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7

Farb, Benson, and Lee Mosher. "Convex cocompact subgroups of mapping class groups." Geometry & Topology 6, no. 1 (2002): 91–152. http://dx.doi.org/10.2140/gt.2002.6.91.

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8

Berrick, A. J., V. Gebhardt, and L. Paris. "Finite index subgroups of mapping class groups." Proceedings of the London Mathematical Society 108, no. 3 (2013): 575–99. http://dx.doi.org/10.1112/plms/pdt022.

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9

Anderson, James W., Javier Aramayona, and Kenneth J. Shackleton. "Free subgroups of surface mapping class groups." Conformal Geometry and Dynamics of the American Mathematical Society 11, no. 04 (2007): 44–55. http://dx.doi.org/10.1090/s1088-4173-07-00156-7.

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10

Franks, John, and Kamlesh Parwani. "Zero entropy subgroups of mapping class groups." Geometriae Dedicata 186, no. 1 (2016): 27–38. http://dx.doi.org/10.1007/s10711-016-0178-9.

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