Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II

Name: Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II
Author: Yuichiro Hoshi, Shinichi Mochizuki
ISBN: 9789811910951

Yuichiro Hoshi, Shinichi Mochizuki

Language: English

Published by Springer Verlag, Singapore, SG, 2022

9811910952 / 9789811910951

Softcover
New

See all details

Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK

5-star seller

AbeBooks seller since June 11, 2025

View this seller's items

Softcover

Condition: New

£ 57.39

£ 65.00 shipping

Ships from United Kingdom to U.S.A.

Quantity: Over 20 available

Add to basket

Free 30-day returns

Save for laterCreate a Want for similar items

Item description from seller

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 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.…

Seller Inventory # LU-9789811910951

Contact seller about this item

Report this item

Title: Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II
Author: Yuichiro Hoshi, Shinichi Mochizuki
Publisher: Springer Verlag, Singapore, SG
Publication year: 2022
Condition: New
Binding: Paperback
Language: English
ISBN 10: 9811910952
ISBN 13: 9789811910951
Edition: 1st ed. 2022.

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 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.

"Synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About the title" may belong to another edition of this title.

Rarewaves.com UK

London, United Kingdom

5-star seller

AbeBooks seller since June 11, 2025

Shipping rates from United Kingdom to U.S.A.

Item	60 to 60 business days	60 to 60 business days
First item	£ 65.00	£ 100.00

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.

Payment methods

Seller's business information

RAREWAVES.COM LIMITED

Elsley Court, 20-22 Great Titchfield Street
London, United Kingdom W1W 8BE

Contact sellerView this seller's itemsView seller's storefront

Right of withdrawal

If you are a consumer you can withdraw from the contract in accordance with the following. Consumer means any natural person who is acting for purposes which are outside his trade, business, craft or profession.

Information regarding the right of withdrawal

Statutory right to withdraw

You have the right to withdraw from this contract within 14 days without giving any reason.

The withdrawal period will expire after 14 days from the day on which you acquire, or a third party other than the carrier and indicated by you acquires, physical possession of the last good or the last lot or piece.

To exercise the right of withdrawal, electronically fill in and submit a clear statement on our website, under "My Purchases" in "My Account". We will communicate to you an acknowledgement of receipt of such a withdrawal on a durable medium (e.g. by e-mail) without delay.

To meet the withdrawal deadline, it is sufficient for you to send your communication concerning your exercise of the right of withdrawal before the withdrawal period has expired.

Effects of withdrawal

If you withdraw from this contract, we will reimburse to you all payments received from you, including the costs of delivery (except for the supplementary costs arising if you chose a type of delivery other than the least expensive type of standard delivery offered by us).

We may make a deduction from the reimbursement for loss in value of any goods supplied, if the loss is the result of unnecessary handling by you.

We will make the reimbursement without undue delay, and not later than 14 days after the day on which we are informed about your decision to withdraw from this contract.

We will make the reimbursement using the same means of payment as you used for the initial transaction, unless you have expressly agreed otherwise; in any event, you will not incur any fees as a result of such reimbursement.

We may withhold reimbursement until we have received the goods back, or you have supplied evidence of having sent back the goods, whichever is the earliest.

You shall send back the goods or hand them over to Rarewaves.com UK, Unit 144 The Lightbox, 111 Power Road, W4 5PY, London, London, United Kingdom, without undue delay and in any event not later than 14 days from the day on which you communicate your withdrawal from this contract to us. The deadline is met if you send back the goods before the period of 14 days has expired. You will have to bear the direct cost of returning the goods. You are only liable for any diminished value of the goods resulting from the handling other than what is necessary to establish the nature, characteristics and functioning of the goods.

Exceptions to the right of withdrawal

The right of withdrawal does not apply to:

The delivery of newspapers, journals or magazines with the exception of subscription contracts; and
The supply of digital content which is not supplied on a tangible medium (e.g. on a CD or DVD) if you accepted when you placed your order that we could start to deliver it, and that you could not withdraw once delivery had started.

Shipping terms

Please note that we do not offer Priority shipping to any country.

We currently do not ship to the below countries:

Russia
Belarus
Ukraine

Please do not attempt to place orders with any of these countries as a ship to address - they will be cancelled.