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Surveys on Surgery Theory (AM-149), Volume 2
  • Language: en
  • Pages: 446

Surveys on Surgery Theory (AM-149), Volume 2

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes res...

Surveys on Surgery Theory
  • Language: en
  • Pages: 447

Surveys on Surgery Theory

Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Talent Abounds
  • Language: en
  • Pages: 268

Talent Abounds

  • Type: Book
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  • Published: 2015-11-17
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  • Publisher: Routledge

How can youthful talent become world-class talent? Talent Abounds tells the stories of master teachers and their students who raise performance to peak levels in classical music and conducting, jazz, opera, modern dance, chess, mathematics, swimming and diving, and the culinary arts. The book is unique in its scope and depth of exploration of different fields of endeavor and the individuals who have shaped them. Readers hear the voices of famous performers, from Leonard Bernstein to Joshua Bell and Mark Spitz, as they describe their early family experiences and formative years, the progression of teachers and coaches they had, their performance careers, educational philosophy and teaching pr...

Geometry and Topology
  • Language: en
  • Pages: 370

Geometry and Topology

  • Type: Book
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  • Published: 2020-12-18
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  • Publisher: CRC Press

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.

Archimedes in the 21st Century
  • Language: en
  • Pages: 160

Archimedes in the 21st Century

  • Type: Book
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  • Published: 2017-08-26
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  • Publisher: Birkhäuser

​This book is a collection of papers presented at the “Archimedes in the 21st Century” world conference, held at the Courant Institute of Mathematical Sciences in 2013. This conference focused on the enduring and continuing influence of Archimedes in our modern world, celebrating his centuries of influence on mathematics, science, and engineering. Archimedes planted the seeds for a myriad of seminal ideas that would grow over the ages. Each chapter surveys the growth of one or more of these seeds, and the fruit that they continue to bear to this day. The conference speakers contributing to this book are actively involved in STEM fields whose origins trace back to Archimedes, many of wh...

Prospects in Topology (AM-138), Volume 138
  • Language: en
  • Pages: 340

Prospects in Topology (AM-138), Volume 138

This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties, including tools for the analysis of group actions on manifolds, calculations of algebraic K-theory, a result on analytic structures on Lie group actions, a presentation of the significance of Dirac operators in smoothing theory, a discussion of the stable topology of 4-manifolds, an answer to the famous question about symmetries of simply connected manifolds, and a fresh perspective on the topological classification of linear transformations. The contributors include A. Adem, A. H. Assadi, M. Bökstedt, S. E. Cappell, R. Charney, M. W. Davis, P. J. Eccles, M. H. Freedman, I. Hambleton, J. C. Hausmann, S. Illman, G. Katz, M. Kreck, W. Lück, I. Madsen, R. J. Milgram, J. Morava, E. K. Pedersen, V. Puppe, F. Quinn, A. Ranicki, J. L. Shaneson, D. Sullivan, P. Teichner, Z. Wang, and S. Weinberger.

Group Actions on Manifolds
  • Language: en
  • Pages: 568

Group Actions on Manifolds

Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable. The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado. A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgment of the work and influence of D. Montgomery on the subject.

Variations on a Theme of Borel
  • Language: en
  • Pages: 365

Variations on a Theme of Borel

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Algebraic Theory of the Bianchi Groups
  • Language: en
  • Pages: 272

Algebraic Theory of the Bianchi Groups

  • Type: Book
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  • Published: 1989-07-17
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  • Publisher: CRC Press

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Tel Aviv Topology Conference: Rothenberg Festschrift
  • Language: en
  • Pages: 334

Tel Aviv Topology Conference: Rothenberg Festschrift

This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.