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8 - Poincaré Duality

Published online by Cambridge University Press:  18 September 2020

Greg Friedman
Affiliation:
Texas Christian University
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Summary

We show that oriented pseudomanifolds possess fundamental intersection homology classes, and we prove that intersection homology possesses a Poincaré duality given by the cap product with the fundamental class. We also prove Lefschetz duality for pseudomanifolds with boundary. We derive from both of these dualities nonsingular cup product and torsion pairings. We include an expositional survey of intersection pairings and the original approach of Goresky and MacPherson to intersection homology duality using such pairings.

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Publisher: Cambridge University Press
Print publication year: 2020

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  • Poincaré Duality
  • Greg Friedman, Texas Christian University
  • Book: Singular Intersection Homology
  • Online publication: 18 September 2020
  • Chapter DOI: https://doi.org/10.1017/9781316584446.009
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  • Poincaré Duality
  • Greg Friedman, Texas Christian University
  • Book: Singular Intersection Homology
  • Online publication: 18 September 2020
  • Chapter DOI: https://doi.org/10.1017/9781316584446.009
Available formats
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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.

  • Poincaré Duality
  • Greg Friedman, Texas Christian University
  • Book: Singular Intersection Homology
  • Online publication: 18 September 2020
  • Chapter DOI: https://doi.org/10.1017/9781316584446.009
Available formats
×