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Topological Library

Author: Sergeĭ Petrovich Novikov

Publisher: World Scientific

Published: 2010

Total Pages: 278

ISBN-13: 981283687X

1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby

Topological Library

Author: Serge? Petrovich Novikov

Publisher: World Scientific

Published: 2012

Total Pages: 590

ISBN-13: 9814401315

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The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces."

Topological Library - Part 1: Cobordisms And Their Applications

Author: Serguei Petrovich Novikov

Publisher: World Scientific

Published: 2007-07-09

Total Pages: 386

ISBN-13: 9814475955

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This is the first of three volumes collecting the original and now classic works in topology written in the 50s-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “Singular homologies of fibre spaces.”This is the translation of the Russian edition published in 2005 with one entry (Milnor's lectures on the h-cobordism) omitted.

Topological Library - Part 2: Characteristic Classes And Smooth Structures On Manifolds

Author: Serguei Petrovich Novikov

Publisher: World Scientific

Published: 2009-10-07

Total Pages: 278

ISBN-13: 9814469297

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This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”

Topological Library

Author: Сергей Петрович Новиков

Publisher: World Scientific Publishing Company

Published: 2007

Total Pages: 396

ISBN-13:

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Topological Library - Part 3: Spectral Sequences In Topology

Author: Serguei Petrovich Novikov

Publisher: World Scientific

Published: 2012-07-25

Total Pages: 590

ISBN-13: 9814401323

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The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”

Elementary Concepts of Topology

Author: Paul Alexandroff

Publisher: Courier Corporation

Published: 2012-08-13

Total Pages: 68

ISBN-13: 0486155064

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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Topological Library: Characteristic classes and smooth structures on manifolds

Author: Serge? Petrovich Novikov

Publisher: World Scientific

Published: 2009-10-01

Total Pages: 278

ISBN-13: 9812836861

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This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s?1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated ?singular homologies of fiber spaces.?

A Topological Picturebook

Author: George K. Francis

Publisher: Springer Science & Business Media

Published: 2013-03-19

Total Pages: 211

ISBN-13: 0387681205

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Praise for George Francis's A Topological Picturebook: Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what ``hands on'' really means. - John Stillwell, University of San Francisco The Topological Picturebook has taught a whole generation of mathematicians to draw, to see, and to think. - Tony Robbin, artist and author of Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought The classic reference for how to present topological information visually, full of amazing hand-drawn pictures of complicated surfaces. - John Sullivan, Technische Universitat Berlin A Topological Picturebook lets students see topology as the original discoverers conceived it: concrete and visual, free of the formalism that burdens conventional textbooks. - Jeffrey Weeks, author of The Shape of Space A Topological Picturebook is a visual feast for anyone concerned with mathematical images. Francis provides exquisite examples to build one's "visualization muscles". At the same time, he explains the underlying principles and design techniques for readers to create their own lucid drawings. - George W. Hart, Stony Brook University In this collection of narrative gems and intriguing hand-drawn pictures, George Francis demonstrates the chicken-and-egg relationship, in mathematics, of image and text. Since the book was first published, the case for pictures in mathematics has been won, and now it is time to reflect on their meaning. A Topological Picturebook remains indispensable. - Marjorie Senechal, Smith College and co-editor of the Mathematical Intelligencer

The Topological Imagination

Author: Angus Fletcher

Publisher: Harvard University Press

Published: 2016-04-04

Total Pages: 327

ISBN-13: 0674968867

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Boldly original and boundary defining, The Topological Imagination clears a space for an intellectual encounter with the shape of human imagining. Joining two commonly opposed domains, literature and mathematics, Angus Fletcher maps the imagination’s ever-ramifying contours and dimensions, and along the way compels us to re-envision our human existence on the most unusual sphere ever imagined, Earth. Words and numbers are the twin powers that create value in our world. Poetry and other forms of creative literature stretch our ability to evaluate through the use of metaphors. In this sense, the literary imagination aligns with topology, the branch of mathematics that studies shape and space. Topology grasps the quality of geometries rather than their quantifiable measurements. It envisions how shapes can be bent, twisted, or stretched without losing contact with their original forms—one of the discoveries of the eighteenth-century mathematician Leonhard Euler, whose Polyhedron Theorem demonstrated how shapes preserve “permanence in change,” like an aging though familiar face. The mysterious dimensionality of our existence, Fletcher says, is connected to our inhabiting a world that also inhabits us. Theories of cyclical history reflect circulatory biological patterns; the day-night cycle shapes our adaptive, emergent patterns of thought; the topology of islands shapes the evolution of evolutionary theory. Connecting literature, philosophy, mathematics, and science, The Topological Imagination is an urgent and transformative work, and a profound invitation to thought.