Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory written by Ulrich Bunke 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 2021-06-21 with Education categories.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Differential Characters
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Author : Christian Bär
language : en
Publisher: Springer
Release Date : 2014-07-31
Differential Characters written by Christian Bär and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with Mathematics categories.
Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized
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Author : Domenico Fiorenza
language : en
Publisher: World Scientific
Release Date : 2023-08-11
Character Map In Non Abelian Cohomology The Twisted Differential And Generalized written by Domenico Fiorenza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-11 with Mathematics categories.
This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
Hamiltonian Perturbation Theory For Ultra Differentiable Functions
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Author : Abed Bounemoura
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21
Hamiltonian Perturbation Theory For Ultra Differentiable Functions written by Abed Bounemoura 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 2021-07-21 with Education categories.
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity
Spectral Expansions Of Non Self Adjoint Generalized Laguerre Semigroups
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Author : Pierre Patie
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-16
Spectral Expansions Of Non Self Adjoint Generalized Laguerre Semigroups written by Pierre Patie and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.
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Homotopy Theory With Bornological Coarse Spaces
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Author : Ulrich Bunke
language : en
Publisher: Springer Nature
Release Date : 2020-09-03
Homotopy Theory With Bornological Coarse Spaces written by Ulrich Bunke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-03 with Mathematics categories.
Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories.
Decoupling On The Wiener Space Related Besov Spaces And Applications To Bsdes
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Author : Stefan Geiss
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-16
Decoupling On The Wiener Space Related Besov Spaces And Applications To Bsdes written by Stefan Geiss and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.
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Cell Complexes Poset Topology And The Representation Theory Of Algebras Arising In Algebraic Combinatorics And Discrete Geometry
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Author : Stuart Margolis
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-30
Cell Complexes Poset Topology And The Representation Theory Of Algebras Arising In Algebraic Combinatorics And Discrete Geometry written by Stuart Margolis and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
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Elliptic Theory For Sets With Higher Co Dimensional Boundaries
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Author : Guy David
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-30
Elliptic Theory For Sets With Higher Co Dimensional Boundaries written by Guy David and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
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On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Two Parameter Generalization Of The Riemann Zeta Function
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Author : Athanassios S. Fokas
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
On The Asymptotics To All Orders Of The Riemann Zeta Function And Of A Two Parameter Generalization Of The Riemann Zeta Function written by Athanassios S. Fokas and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Mathematics categories.
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