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Quotient and blow-up of automorphisms of graphs of groups
- Publication Year :
- 2015
- Publisher :
- HAL CCSD, 2015.
-
Abstract
- In this paper, we study the quotient and “blow-up” of graph-of-groups [Formula: see text] and of their automorphisms [Formula: see text]. We show that the existence of such a blow-up of any [Formula: see text], relative to a given family of “local” graph-of-groups isomorphisms [Formula: see text] depends crucially on the [Formula: see text]-conjugacy class of the correction term [Formula: see text] for any edge [Formula: see text] of [Formula: see text], where [Formula: see text]-conjugacy is a new but natural concept introduced here. As an application, we obtain a criterion as to whether a partial Dehn twist can be blown up relative to local Dehn twists, to give an actual Dehn twist. The results of this paper are also used crucially in the follow-up papers [Lustig and Ye, Normal form and parabolic dynamics for quadratically growing automorphisms of free groups, arXiv:1705.04110v2; Ye, Partial Dehn twists of free groups relative to local Dehn twists — A dichotomy, arXiv:1605.04479 ; When is a polynomially growing automorphism of [Formula: see text] geometric, arXiv:1605.07390 ].
- Subjects :
- Bass-Serre theory
General Mathematics
010102 general mathematics
High Energy Physics::Phenomenology
graph-of-groups
Dehn twists
Group Theory (math.GR)
0102 computer and information sciences
Automorphism
01 natural sciences
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
Combinatorics
Mathematics::Group Theory
Dehn twist
010201 computation theory & mathematics
free group
FOS: Mathematics
0101 mathematics
Mathematics - Group Theory
20Fxx
20Exx
Quotient
[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....8b9e100862a4868c62e9c08c1114086f