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Introductory Lectures on Equivariant Cohomology(AMS-204)$
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Loring W. Tu

Print publication date: 2020

Print ISBN-13: 9780691191751

Published to Princeton Scholarship Online: January 2021

DOI: 10.23943/princeton/9780691191751.001.0001

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Spectral Sequences

Spectral Sequences

Chapter:
(p.45) Chapter Six Spectral Sequences
Source:
Introductory Lectures on Equivariant Cohomology
Author(s):

Loring W. Tu

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691191751.003.0006

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined by Jean-Louis Koszul, Henri Cartan, Jean-Pierre Serre, and many others. The chapter provides a short introduction, without proofs, to spectral sequences. As an example, it computes the cohomology of the complex projective plane. The chapter then details Leray's theorem. A spectral sequence is like a book with many pages. Each time one turns a page, one obtains a new page that is the cohomology of the previous page.

Keywords:   spectral sequences, fiber bundles, Jean Leray, cohomology, complex projective plane, Leray's theorem, computational tool

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