Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
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Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
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Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture written by Joel Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.
Languages And Automata
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Author : Benjamin Steinberg
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-10-21
Languages And Automata written by Benjamin Steinberg and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-21 with Mathematics categories.
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
Homological Mirror Symmetry For The Quartic Surface
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Author : Paul Seidel
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Homological Mirror Symmetry For The Quartic Surface written by Paul Seidel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
The author proves Kontsevich's form of the mirror symmetry conjecture for (on the symplectic geometry side) a quartic surface in C .
Topics In Groups And Geometry
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Topics In Groups And Geometry written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Geometric Group Theory
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Author : Clara Löh
language : en
Publisher: Springer
Release Date : 2017-12-19
Geometric Group Theory written by Clara Löh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
On Non Topological Solutions Of The A 2 And B 2 Chern Simons System
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Author : Weiwei Ao
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
On Non Topological Solutions Of The A 2 And B 2 Chern Simons System written by Weiwei Ao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.
Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography
Higher Moments Of Banach Space Valued Random Variables
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Author : Svante Janson
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
Higher Moments Of Banach Space Valued Random Variables written by Svante Janson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Mathematics categories.
The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
Stability Of Line Solitons For The Kp Ii Equation In Mathbb R 2
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Author : Tetsu Mizumachi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
Stability Of Line Solitons For The Kp Ii Equation In Mathbb R 2 written by Tetsu Mizumachi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Mathematics categories.
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.
Irreducible Geometric Subgroups Of Classical Algebraic Groups
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Author : Timothy C. Burness,
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
Irreducible Geometric Subgroups Of Classical Algebraic Groups written by Timothy C. Burness, and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
Global Carleman Estimates For Degenerate Parabolic Operators With Applications
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Author : P. Cannarsa
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25
Global Carleman Estimates For Degenerate Parabolic Operators With Applications written by P. Cannarsa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.
Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.