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Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves ...
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Item specifics
- Condition
- Book Title
- Topics Surrounding the Combinatorial Anabelian Geometry of Hyperb
- ISBN
- 9789811910951
- Subject Area
- Mathematics
- Publication Name
- Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II : Tripods and Combinatorial Cuspidalization
- Item Length
- 9.3 in
- Publisher
- Springer
- Subject
- General, Number Theory, Geometry / Algebraic
- Publication Year
- 2022
- Series
- Lecture Notes in Mathematics Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Width
- 6.1 in
- Item Weight
- 9.8 Oz
- Number of Pages
- Xxiii, 150 Pages
About this product
Product Information
The 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 induces the 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.
Product Identifiers
Publisher
Springer
ISBN-10
9811910952
ISBN-13
9789811910951
eBay Product ID (ePID)
25057252439
Product Key Features
Publication Name
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II : Tripods and Combinatorial Cuspidalization
Format
Trade Paperback
Language
English
Subject
General, Number Theory, Geometry / Algebraic
Publication Year
2022
Series
Lecture Notes in Mathematics Ser.
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xxiii, 150 Pages
Dimensions
Item Length
9.3 in
Item Width
6.1 in
Item Weight
9.8 Oz
Additional Product Features
Series Volume Number
2299
Number of Volumes
1 Vol.
Lc Classification Number
Qa241-247.5
Table of Content
1. 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.
Copyright Date
2022
Dewey Decimal
516.13
Dewey Edition
23
Illustrated
Yes
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