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On the automorphism group of the asymptotic pants complex of an infinite surface of genus zero
Author(s) -
Funar Louis,
Nguyen Maxime
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300243
Subject(s) - mathematics , genus , automorphism , zero (linguistics) , group (periodic table) , mapping class group , class (philosophy) , automorphism group , combinatorics , pure mathematics , type (biology) , surface (topology) , set (abstract data type) , outer automorphism group , discrete mathematics , geometry , artificial intelligence , computer science , biology , ecology , linguistics , philosophy , botany , chemistry , organic chemistry , programming language
The braided Thompson group B 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 vertices are asymptotically trivial pants decompositions. We prove that the automorphism groupB 1 2 ̂ of this complex is also an asymptotic mapping class group in a weaker sense. MoreoverB 1 2 ̂ is obtained by B by first adding new elements called half‐twists and further completing it.