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Lecture Notes in Mathematics Ser.: Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II : Tripods and Combinatorial Cuspidalization by Yuichiro Hoshi and Shinichi Mochizuki (2022, Trade Paperback)
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About this product
Product Identifiers
PublisherSpringer
ISBN-109811910952
ISBN-139789811910951
eBay Product ID (ePID)25057252439
Product Key Features
Number of PagesXxiii, 150 Pages
LanguageEnglish
Publication NameTopics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II : Tripods and Combinatorial Cuspidalization
Publication Year2022
SubjectGeneral, Number Theory, Geometry / Algebraic
TypeTextbook
Subject AreaMathematics
AuthorYuichiro Hoshi, Shinichi Mochizuki
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight9.8 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Dewey Edition23
Series Volume Number2299
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.13
Table Of Content1. Combinatorial Anabelian Geometry in the Absence of Group-theoretic Cuspidality.- 2. Partial Combinatorial Cuspidalization for F-admissible Outomorphisms.- 3. Synchronization of Tripods.- 4. Glueability of Combinatorial Cuspidalizations. References.
SynopsisThe present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero. The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space. We then turn to the study of tripod synchronization , i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve inducesthe same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists . In the final portion of the monograph, we develop a theory of localizability , on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
LC Classification NumberQA241-247.5
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