Essential Topology

  • Martin D. Crossley

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Martin D. Crossley
    Pages 1-2
  3. Martin D. Crossley
    Pages 3-14
  4. Martin D. Crossley
    Pages 15-34
  5. Martin D. Crossley
    Pages 37-53
  6. Martin D. Crossley
    Pages 55-88
  7. Martin D. Crossley
    Pages 91-116
  8. Martin D. Crossley
    Pages 117-126
  9. Martin D. Crossley
    Pages 127-148
  10. Martin D. Crossley
    Pages 149-166
  11. Martin D. Crossley
    Pages 167-197
  12. Martin D. Crossley
    Pages 199-214
  13. Back Matter
    Pages 215-226

About this book

Introduction

Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.

While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.

With chapters on:

* continuity and topological spaces

* deconstructionist topology

* the Euler number

* homotopy groups including the fundamental group

* simplicial and singular homology, and

* fibre bundles

Essential Topology contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well prepared for it.

Keywords

Algebraic topology Continuity Fundamental group Homology Homotopy Homotopy group Topological space Topology Vector fields

Authors and affiliations

  • Martin D. Crossley
    • 1
  1. 1.Department of MathematicsUniversity of Wales SwanseaSwanseaUK

Bibliographic information

  • DOI https://doi.org/10.1007/1-84628-194-6
  • Copyright Information Springer-Verlag London Limited 2005
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-85233-782-7
  • Online ISBN 978-1-84628-194-5
  • Series Print ISSN 1615-2085
  • About this book