Higher Homotopy Structures in Topology and Mathematical Physics

Higher Homotopy Structures in Topology and Mathematical Physics PDF

Author: James D. Stasheff

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 321

ISBN-13: 082180913X

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Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas. It's features include: accessible to a broad audience interested in mathematics and physics; offers a comprehensive overview of Stasheff's work; and, contains papers on very current research topics, including operads, combinatorial polyhedra and moduli spaces.

Advances in Homotopy Theory

Advances in Homotopy Theory PDF

Author: Ioan Mackenzie James

Publisher: Cambridge University Press

Published: 1989-12-07

Total Pages: 196

ISBN-13: 9780521379076

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This volume records the lectures given at a conference to celebrate Professor Ioan James' 60th birthday.

History of Topology

History of Topology PDF

Author: I.M. James

Publisher: Elsevier

Published: 1999-08-24

Total Pages: 1067

ISBN-13: 0080534074

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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Algebraic Methods in Unstable Homotopy Theory

Algebraic Methods in Unstable Homotopy Theory PDF

Author: Joseph Neisendorfer

Publisher: Cambridge University Press

Published: 2010-02-18

Total Pages: 575

ISBN-13: 1139482599

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The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.

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