Introduction to Topological Manifolds

This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develo...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lee, John (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2011.
Edición:2nd ed. 2011.
Colección:Graduate Texts in Mathematics, 202
Temas:
Manifolds (Mathematics).
Algebraic topology.
Manifolds and Cell Complexes.
Algebraic Topology.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Introduction to Topological Manifolds  |h [electronic resource] /  |c by John Lee. 
250 |a 2nd ed. 2011. 
264 1 |a New York, NY :  |b Springer New York :  |b Imprint: Springer,  |c 2011. 
300 |a XVII, 433 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Graduate Texts in Mathematics,  |x 2197-5612 ;  |v 202 
505 0 |a Preface -- 1 Introduction -- 2 Topological Spaces -- 3 New Spaces from Old -- 4 Connectedness and Compactness -- 5 Cell Complexes -- 6 Compact Surfaces -- 7 Homotopy and the Fundamental Group -- 8 The Circle -- 9 Some Group Theory -- 10 The Seifert-Van Kampen Theorem -- 11 Covering Maps -- 12 Group Actions and Covering Maps -- 13 Homology -- Appendix A: Review of Set Theory -- Appendix B: Review of Metric Spaces -- Appendix C: Review of Group Theory -- References -- Notation Index -- Subject Index. 
520 |a This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author's book Introduction to Smooth Manifolds is meant to act as a sequel to this book. 
650 0 |a Manifolds (Mathematics). 
650 0 |a Algebraic topology. 
650 1 4 |a Manifolds and Cell Complexes. 
650 2 4 |a Algebraic Topology. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9781441979391 
776 0 8 |i Printed edition:  |z 9781441979414 
776 0 8 |i Printed edition:  |z 9781461427902 
830 0 |a Graduate Texts in Mathematics,  |x 2197-5612 ;  |v 202 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-1-4419-7940-7  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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