On Dynamical Poisson Groupoids
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On Dynamical Poisson Groupoids I
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Author : Luen-Chau Li
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
On Dynamical Poisson Groupoids I written by Luen-Chau Li 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 2005 with Mathematics categories.
We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors.
On Dynamical Poisson Groupoids
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Author : Luen-Chau Li
language : en
Publisher:
Release Date : 2005
On Dynamical Poisson Groupoids written by Luen-Chau Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
The Breadth Of Symplectic And Poisson Geometry
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Author : Jerrold E. Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-03
The Breadth Of Symplectic And Poisson Geometry written by Jerrold E. Marsden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-03 with Mathematics categories.
* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics
General Theory Of Lie Groupoids And Lie Algebroids
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Author : Kirill C. H. Mackenzie
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-09
General Theory Of Lie Groupoids And Lie Algebroids written by Kirill C. H. Mackenzie 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 2005-06-09 with Mathematics categories.
This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.
A Generating Function Approach To The Enumeration Of Matrices In Classical Groups Over Finite Fields
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Author : Jason Fulman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
A Generating Function Approach To The Enumeration Of Matrices In Classical Groups Over Finite Fields written by Jason Fulman 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 2005 with Mathematics categories.
Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.
Geometry Mechanics And Dynamics
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Author : Dong Eui Chang
language : en
Publisher: Springer
Release Date : 2015-04-16
Geometry Mechanics And Dynamics written by Dong Eui Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups
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Author : Jie Wu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups written by Jie Wu 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.
The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie$(n)$, as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.
Equivalences Of Classifying Spaces Completed At The Prime Two
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Author : Robert Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Equivalences Of Classifying Spaces Completed At The Prime Two written by Robert Oliver 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.
We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.
Weil Petersson Metric On The Universal Teichmuller Space
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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Weil Petersson Metric On The Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n 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 this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
The Beilinson Complex And Canonical Rings Of Irregular Surfaces
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Author : Alberto Canonaco
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Beilinson Complex And Canonical Rings Of Irregular Surfaces written by Alberto Canonaco 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.
An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant