Diffeomorphisms Analytic Torsion And Noncommutative Geometry
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Diffeomorphisms Analytic Torsion And Noncommutative Geometry
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Author : John Lott
language : en
Publisher:
Release Date : 1996
Diffeomorphisms Analytic Torsion And Noncommutative Geometry written by John Lott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Diffeomorphisms And Noncommutative Analytic Torsion
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Author : John Lott
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Diffeomorphisms And Noncommutative Analytic Torsion written by John Lott 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 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians working in global analysis and analysis on manifolds
Surveys In Noncommutative Geometry
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Author : Nigel Higson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Surveys In Noncommutative Geometry written by Nigel Higson 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 2006 with Mathematics categories.
In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ordinary geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the residue index theorem of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area.
Bulletin New Series Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1997
Bulletin New Series Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
A Geometric Setting For Hamiltonian Perturbation Theory
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Author : Anthony D. Blaom
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
A Geometric Setting For Hamiltonian Perturbation Theory written by Anthony D. Blaom 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 2001 with Mathematics categories.
In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
Bulletin Of The American Mathematical Society
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Author :
language : en
Publisher:
Release Date : 1997
Bulletin Of The American Mathematical Society written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Analytic Quotients
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Author : Ilijas Farah
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Analytic Quotients written by Ilijas Farah 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 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in set theory.
Noncommutative Maslov Index And Eta Forms
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Author : Charlotte Wahl
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Noncommutative Maslov Index And Eta Forms written by Charlotte Wahl 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 2007 with Mathematics categories.
The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a $C*$-algebra $\mathcal{A $, is an element in $K 0(\mathcal{A )$. The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of $\mathcal{A $. The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an $\mathcal{A $-vector bundle. The author develops an analytic framework for this type of index problem.
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures
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Author : Vicente Cortés
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures written by Vicente Cortés 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 2000 with Mathematics categories.
Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
Integrable Systems And Algebraic Geometry
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Author : Ron Donagi
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-02
Integrable Systems And Algebraic Geometry written by Ron Donagi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Mathematics categories.
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.