The Novikov Conjecture

Author : Matthias Kreck
Publisher : Springer Science & Business Media
ISBN 13 : 3764373156
Total Pages : 268 pages
Book Rating : 4.53/5 ( download)

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Download or read book The Novikov Conjecture written by Matthias Kreck and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.

Author : Steven C. Ferry
Publisher : Cambridge University Press
ISBN 13 : 0521497957
Total Pages : 378 pages
Book Rating : 4.54/5 ( download)

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Download or read book Novikov Conjectures, Index Theorems, and Rigidity: Volume 2 written by Steven C. Ferry and published by Cambridge University Press. This book was released on 1995-11-23 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of `Novikov conjectures, index theorems and rigidity'.

Author : Steven C. Ferry
Publisher : Cambridge University Press
ISBN 13 : 0521497965
Total Pages : 386 pages
Book Rating : 4.61/5 ( download)

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Download or read book Novikov Conjectures, Index Theorems, and Rigidity: Volume 1 written by Steven C. Ferry and published by Cambridge University Press. This book was released on 1995-11-23 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Author : Helmut Hofer
Publisher : Birkhäuser
ISBN 13 : 3034892179
Total Pages : 688 pages
Book Rating : 4.79/5 ( download)

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Download or read book The Floer Memorial Volume written by Helmut Hofer and published by Birkhäuser. This book was released on 2012-12-06 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder.

Author : Steven C. Ferry
Publisher : Cambridge University Press
ISBN 13 : 0521497965
Total Pages : 386 pages
Book Rating : 4.61/5 ( download)

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Download or read book Novikov Conjectures, Index Theorems, and Rigidity: Volume 1 written by Steven C. Ferry and published by Cambridge University Press. This book was released on 1995-11-23 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Author : Alain Connes
Publisher : Springer Science & Business Media
ISBN 13 : 9783540203575
Total Pages : 372 pages
Book Rating : 4.75/5 ( download)

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Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
ISBN 13 : 1470472937
Total Pages : 417 pages
Book Rating : 4.31/5 ( download)

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Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Society. This book was released on 2023-02-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author : V. M. Buchstaber
Publisher : American Mathematical Soc.
ISBN 13 : 9780821806661
Total Pages : 204 pages
Book Rating : 4.61/5 ( download)

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Download or read book Solitons, Geometry, and Topology: On the Crossroad written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 1997 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Shmuel Weinberger
Publisher : Cambridge University Press
ISBN 13 : 1108916848
Total Pages : 366 pages
Book Rating : 4.44/5 ( download)

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Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by Cambridge University Press. This book was released on 2022-12-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.