Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T03:30:34.768Z Has data issue: false hasContentIssue false

4 - Basic Properties of Singular and PL Intersection Homology

Published online by Cambridge University Press:  18 September 2020

Greg Friedman
Affiliation:
Texas Christian University
Get access

Summary

We develop the basic properties of PL and singular intersection homology. This includes the behavior of the intersection homology groups under stratified maps and homotopies and the invariance of intersection homology groups under stratified homotopy equivalences. We introduce relative intersection homology, the long exact sequence of a pair, Mayer–Vietoris sequences, and excision. An important special computation is that of the intersection homology of a cone, which provides a good basic example of an intersection homology computation but also provides a formula that plays an essential role throughout the theory, as all points in pseudomanifolds have neighborhoods that are stratified homotopy equivalent to cones.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×