String Topology And Cyclic Homology
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String Topology And Cyclic Homology
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Author : Ralph L. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
String Topology And Cyclic Homology written by Ralph L. Cohen 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 2006-03-21 with Mathematics categories.
This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.
Alpine Perspectives On Algebraic Topology
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Author : Christian Ausoni
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Alpine Perspectives On Algebraic Topology written by Christian Ausoni 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 2009 with Mathematics categories.
Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.
Algebraic Topology
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Author : H.V. Hưng Nguyễn
language : en
Publisher: Springer
Release Date : 2018-01-02
Algebraic Topology written by H.V. Hưng Nguyễn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by PhD students and experts in the field. Among the three contributions, two concern stable homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-localization and the cohomology of the Morava stabilizer groups. Powell’s chapter is concerned with the derived functors of the destabilization and iterated loop functors and provides a small complex to compute them. Indications are given for the odd prime case. Providing an introduction to some aspects of string and brane topology, Ginot’s contribution focusses on Hochschild homology and its generalizations. It contains a number of new results and fills a gap in the literature.
Perturbed Gradient Flow Trees And A Algebra Structures In Morse Cohomology
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Author : Stephan Mescher
language : en
Publisher: Springer
Release Date : 2018-04-25
Perturbed Gradient Flow Trees And A Algebra Structures In Morse Cohomology written by Stephan Mescher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-25 with Mathematics categories.
This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid’s approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
New Perspectives And Challenges In Symplectic Field Theory
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Author : Miguel Abreu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
New Perspectives And Challenges In Symplectic Field Theory written by Miguel Abreu 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 2009 with Mathematics categories.
This volume, in honor of Yakov Eliashberg, gives a panorama of some of the most fascinating recent developments in symplectic, contact and gauge theories. It contains research papers aimed at experts, as well as a series of skillfully written surveys accessible for a broad geometrically oriented readership from the graduate level onwards. This collection will serve as an enduring source of information and ideas for those who want to enter this exciting area as well as for experts.
Deformation Spaces
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Author : Hossein Abbaspour
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-21
Deformation Spaces written by Hossein Abbaspour 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 2010-04-21 with Mathematics categories.
The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.
Global Differential Geometry
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Author : Christian Bär
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-18
Global Differential Geometry written by Christian Bär 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 2011-12-18 with Mathematics categories.
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Cyclic Homology In Non Commutative Geometry
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-17
Cyclic Homology In Non Commutative Geometry written by Joachim Cuntz 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 2003-11-17 with Mathematics categories.
Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
A Foundation For Props Algebras And Modules
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Author : Donald Yau
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-05-28
A Foundation For Props Algebras And Modules written by Donald Yau 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 2015-05-28 with Mathematics categories.
PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.