Skip to main content

Homological Algebra

  • Chapter
Computational Homology

Part of the book series: Applied Mathematical Sciences ((AMS,volume 157))

  • 2457 Accesses

Abstract

We finished the previous chapter with the observation that given a space X and a subset A it would be useful to have a means of computing the number of components of X that are disjoint from A. Using this as motivation, in Section 9.1 we introduce the concept of relative homology. Though motivated by a simple problem, it turns out that relative homology is an extremely powerful tool, both as a means of extracting topology from the homological algebra and as an abstract computational technique. The language of these computational methods takes the form of exact sequences, which are discussed in Section 9.2.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Kaczynski, T., Mischaikow, K., Mrozek, M. (2004). Homological Algebra. In: Computational Homology. Applied Mathematical Sciences, vol 157. Springer, New York, NY. https://doi.org/10.1007/0-387-21597-2_9

Download citation

  • DOI: https://doi.org/10.1007/0-387-21597-2_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2354-7

  • Online ISBN: 978-0-387-21597-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics