Quotients of the mapping class group by power subgroups

Autor: Louis Funar, Javier Aramayona

Publikováno v: Bulletin of the London Mathematical Society
Bulletin of the London Mathematical Society, London Mathematical Society, 2019, 51 (3), pp.385-398. ⟨10.1112/blms.12236⟩
Digital.CSIC. Repositorio Institucional del CSIC
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We study the quotient of the mapping class group $\operatorname{Mod}_g^n$ of a surface of genus $g$ with $n$ punctures, by the subgroup $\operatorname{Mod}_g^n[p]$ generated by the $p$-th powers of Dehn twists. Our first main result is that $\operato

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ab21b1ea319ac2c5f98fb1c291a1db1a
https://hal.archives-ouvertes.fr/hal-01992036

On the automorphism group of the asymptotic pants complex of an infinite surface of genus zero

Autor: Louis Funar, Maxime Nguyen

Publikováno v: Mathematische Nachrichten. 289:1189-1207

The braided Thompson group is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher–Thurston cell complex whose ve

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https://doi.org/10.1002/mana.201300243

Manifolds which admit maps with finitely many critical points into spheres of small dimensions

Autor: Louis Funar, Cornel Pintea

Publikováno v: Michigan Mathematical Journal
Michigan Mathematical Journal, University of Michigan, 2018, 67 (3), pp.585-615. ⟨10.1307/mmj/1529460326⟩
Michigan Mathematical Journal, University of Michigan, 2018, 67, pp.585-615
Michigan Math. J. 67, iss. 3 (2018), 585-615

We construct, for $m\geq 6$ and $2n\leq m$, closed manifolds $M^{m}$ with finite nonzero $\varphi(M^{m},S^{n}$), where $\varphi(M,N)$ denotes the minimum number of critical points of a smooth map $M\to N$. We also give some explicit families of examp

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https://hal.archives-ouvertes.fr/hal-01992044

Asymptotic mapping class groups of closed surfaces punctured along Cantor sets

Autor: Javier Aramayona, Louis Funar

Publikováno v: Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2021, 21 (1), pp.1--29. ⟨10.17323/1609-4514-2021-21-1-1-29⟩
Moscow Math. J.
Moscow Math. J., In press
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We introduce subgroups Bg
The first author was partially funded by grants RYC-2013-13008 and MTM2015-67781. He also acknowledges support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 ”RNMS: Geometric Structures and

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05942af90932b3d51c126cb4423672f1
http://arxiv.org/abs/1701.08132

On Burau’s representations at roots of unity

Autor: Toshitake Kohno, Louis Funar

Publikováno v: Geometriae Dedicata. 169:145-163

We consider subgroups of the braid groups which are generated by $$n$$ th powers of the standard generators and prove that any infinite intersection (with even $$n$$ ) is trivial. This is motivated by some conjectures of Squier concerning the kernels

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https://doi.org/10.1007/s10711-013-9847-0