Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Springer Monographs in Mathematics
cover

Topology of Infinite-Dimensional Manifolds

Authors: Sakai, Katsuro

  • Provides knowledge of fundamental results containing characterizations of various infinite-dimensional manifolds
  • Contains details of most proofs so that graduate students in topology need to make only minimum reference to literature
  • Presents combinatorial ∞-manifolds with their characterization and a proof of the Hauptvermutung for them
see more benefits

Buy this book

eBook $119.00
price for Mexico
  • The eBook version of this title will be available soon
  • Due: 9 de diciembre de 2020
  • ISBN 978-981-15-7575-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $159.99
price for Mexico
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: 11 de noviembre de 2020
  • ISBN 978-981-15-7574-7
  • Free shipping for individuals worldwide. Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering.
  • Immediate ebook access, if available*, with your print order
About this book

An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology).

This book is designed for graduate students to acquire knowledge of fundamental results on infinite-dimensional manifolds and their characterizations. To read and understand this book, some background is required even for senior graduate students in topology, but that background knowledge is minimized and is listed in the first chapter so that references can easily be found. Almost all necessary background information is found in Geometric Aspects of General Topology, the author's first book.

Many kinds of hyperspaces and function spaces are investigated in various branches of mathematics, which are mostly infinite-dimensional. Among them, many examples of infinite-dimensional manifolds have been found. For researchers studying such objects, this book will be very helpful. As outstanding applications of Hilbert cube manifolds, the book contains proofs of the topological invariance of Whitehead torsion and Borsuk’s conjecture on the homotopy type of compact ANRs. This is also the first book that presents combinatorial ∞-manifolds, the infinite-dimensional version of combinatorial n-manifolds, and proofs of two remarkable results, that is, any triangulation of each manifold modeled on the direct limit of Euclidean spaces is a combinatorial ∞-manifold and the Hauptvermutung for them is true.

Buy this book

eBook $119.00
price for Mexico
  • The eBook version of this title will be available soon
  • Due: 9 de diciembre de 2020
  • ISBN 978-981-15-7575-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $159.99
price for Mexico
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: 11 de noviembre de 2020
  • ISBN 978-981-15-7574-7
  • Free shipping for individuals worldwide. Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering.
  • Immediate ebook access, if available*, with your print order
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Topology of Infinite-Dimensional Manifolds
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-7575-4
DOI
10.1007/978-981-15-7575-4
Hardcover ISBN
978-981-15-7574-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XV, 623
Number of Illustrations
134 b/w illustrations
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.