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


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Автор: Denis Fedoseev, Igor Nikonov, Seongjeong Kim, Vassily Olegovich Manturov
Название:  Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory
ISBN: 9789811220111
Издательство: World Scientific Publishing
Классификация:

ISBN-10: 9811220115
Обложка/Формат: Hardcover
Страницы: 388
Вес: 0.68 кг.
Дата издания: 11.05.2020
Серия: Series on knots & everything
Язык: English
Размер: 22.91 x 15.19 x 2.24 cm
Читательская аудитория: Tertiary education (us: college)
Ключевые слова: Analytic topology, MATHEMATICS / Geometry / General,MATHEMATICS / Group Theory,MATHEMATICS / Topology
Рейтинг:
Поставляется из: Англии
Описание:

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 -- Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.



Lecture Notes on Knot Invariants

Автор: Li Weiping
Название: Lecture Notes on Knot Invariants
ISBN: 9814675962 ISBN-13(EAN): 9789814675963
Издательство: World Scientific Publishing
Рейтинг:
Цена: 33790.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:

The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.

With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.


Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces

Автор: Victor Guillemin
Название: Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
ISBN: 0817637702 ISBN-13(EAN): 9780817637705
Издательство: Springer
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Цена: 144410.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G. This book is suitable for researchers and can be used as a semester text.

Invariants of Homology 3-Spheres

Автор: R.V. Gamkrelidze; Nikolai Saveliev; A. Vassiiev
Название: Invariants of Homology 3-Spheres
ISBN: 3642078494 ISBN-13(EAN): 9783642078491
Издательство: Springer
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Цена: 130430.00 T
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Описание: The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism.

Spectral Invariants With Bulk, Quasi-Morphisms and Lagrangian Floer Theory

Автор: Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono
Название: Spectral Invariants With Bulk, Quasi-Morphisms and Lagrangian Floer Theory
ISBN: 1470436256 ISBN-13(EAN): 9781470436254
Издательство: Mare Nostrum (Eurospan)
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Цена: 83160.00 T
Наличие на складе: Нет в наличии.
Описание: Develops various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations - i.e. deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology.

Knot Invariants and Higher Representation Theory

Автор: Ben Webster
Название: Knot Invariants and Higher Representation Theory
ISBN: 1470426501 ISBN-13(EAN): 9781470426507
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
Наличие на складе: Невозможна поставка.
Описание: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ and by Mazorchuk-Stroppel and Sussan for $\mathfrak{sl}_n$.

New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory

Автор: Burghelea Dan
Название: New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory
ISBN: 9814618241 ISBN-13(EAN): 9789814618243
Издательство: World Scientific Publishing
Рейтинг:
Цена: 72870.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents an alternative to what the topologists refer to as "Morse-Novikov theory", a mathematical theory which belongs to the fields of geometry and topology.

An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants

Автор: Paul Feehan, Thomas G. Leness
Название: An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants
ISBN: 147041421X ISBN-13(EAN): 9781470414214
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 80390.00 T
Наличие на складе: Невозможна поставка.
Описание: The authors prove an analogue of the Kotschick-Morgan Conjecture in the context of $\mathrm{SO(3)}$ monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the $\mathrm{SO(3)}$-monopole cobordism.

Knots, Links, Spatial Graphs, and Algebraic Invariants

Автор: Erica Flapan, Allison Henrich, Aaron Kaestner, Sam Nelson
Название: Knots, Links, Spatial Graphs, and Algebraic Invariants
ISBN: 1470428474 ISBN-13(EAN): 9781470428471
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 110880.00 T
Наличие на складе: Невозможна поставка.
Описание: Contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs. Included are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams.

Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures : Conference in Honor of William Jaco`s 70th Birthday, ... Stillwater, OK (Contemporary Mathematics)

Автор: Bartolini Li
Название: Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures : Conference in Honor of William Jaco`s 70th Birthday, ... Stillwater, OK (Contemporary Mathematics)
ISBN: 0821852957 ISBN-13(EAN): 9780821852958
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 72990.00 T
Наличие на складе: Невозможна поставка.
Описание: Aptly named `Television`s First Lady` by Walter Ames of the Los Angeles Times, actress Beverly Garland (1926-2008) is also regarded as a Western and science-fiction film icon. In addition to more than 700 TV appearances, she made more than 55 feature and made-for-television films. This comprehensive biography includes a foreword and afterword by her colleagues Joseph Campanella and Peggy Webber.

Lecture Notes On Knot Invariants

Автор: Li Weiping
Название: Lecture Notes On Knot Invariants
ISBN: 9814675954 ISBN-13(EAN): 9789814675956
Издательство: World Scientific Publishing
Рейтинг:
Цена: 65470.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry.

L2-Invariants: Theory and Applications to Geometry and K-Theory

Автор: Wolfgang L?ck
Название: L2-Invariants: Theory and Applications to Geometry and K-Theory
ISBN: 3642078109 ISBN-13(EAN): 9783642078101
Издательство: Springer
Рейтинг:
Цена: 130390.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material.

Classical and Involutive Invariants of Krull Domains

Автор: M.V. Reyes S?nchez; A. Verschoren
Название: Classical and Involutive Invariants of Krull Domains
ISBN: 9401064946 ISBN-13(EAN): 9789401064941
Издательство: Springer
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.


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