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Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by Igor Nikonov, Seongjeong Kim, Vassily Olegovich Manturov, Denis Fedoseev (Hardcover, 2020)

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ISBN-13: 9789811220111, 978-9811220111. Format: Hardback.

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This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups - nk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

Product Identifiers

Publisher
World Industries Scientific Publishing Co Pte LTD
ISBN-13
9789811220111
eBay Product ID (ePID)
17046676577

Product Key Features

Author
Igor Nikonov, Seongjeong Kim, Vassily Olegovich Manturov, Denis Fedoseev
Publication Name
Invariants and Pictures: Low-Dimensional Topology and Combinatorial Group Theory
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
2020
Type
Textbook
Number of Pages
388 Pages

Dimensions

Volume
66

Additional Product Features

Title_Author
Vassily Olegovich Manturov, Igor Nikonov, Seongjeong Kim, Denis Fedoseev
Series Title
Series on Knots & Everything
Country/Region of Manufacture
Singapore

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Picture 1 of 1

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by Igor Nikonov, Seongjeong Kim, Vassily Olegovich Manturov, Denis Fedoseev (Hardcover, 2020)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Invariants And Pictures: Low-dimensional Topology And Combina... - 9789811220111

item 2 Invariants And Pictures: Low-dimensional Topology And Combinatorial Group

Best Selling in Textbooks

Teaching Good Learner Repertoires by Steve Ward (2013, Trade Paperback)

Designing Data-Intensive Applications : The Big Ideas Behind Reliable, Scalable, and Maintainable Systems by Martin Kleppmann (2017, Trade Paperback)

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Self Heal by Design : The Role of Micro-organisms for Health by Barbara O'Neill (2018, Trade Paperback)

Leadership : Theory and Practice by Peter G. Northouse (2021, Trade Paperback, Revised edition)

Diagnostic and Statistical Manual of Mental Disorders : DSM-5-TR by American Psychiatric Association (2022, Hardcover)

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