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The course will cover the cohomology of topological spaces, with a heavy emphasis on interesting examples, most of which are manifolds.


Autumn 2009 (Monday, October 5 to Friday, December 11)


  • Wed 10:05 - 10:55
  • Thu 10:05 - 10:55


Some knowledge of general topology and commutative rings.


  1. Topological manifolds: definition and examples.
  2. Cohomology rings: basic properties, without construction. Description (without proof) of the cohomology rings of many interesting manifolds.
  3. Cohomology of configuration spaces: partial proof of stated description.
  4. Geometry of balls and spheres.
  5. Geometry of Hermitian spaces.
  6. Cohomology of balls and spheres.
  7. Cohomology of unitary groups.
  8. Cohomology of projective spaces.
  9. Vector bundles.
  10. Smooth structures and the tangent bundle.
  11. The Thom isomorphism theorem.
  12. Homotopical classification of vector bundles and line bundles.
  13. Cohomology of projective bundles; Chern classes; cohomology of flag manifolds and Grassmannians.
  14. Normal bundles, tubular neighbourhoods, and the Pontrjagin-Thom construction.
  15. Poincaré duality.
  16. The universal coefficient theorem.
  17. Cohomology of complex hypersurfaces.


Neil Strickland
Phone (0114) 2223852
Interests Algebraic topology
Photo of Neil Strickland
Profile: Jitesh Gajjar and I are the two instigators of the MAGIC project.

I am interested in Algebraic Topology and Stable Homotopy Theory.


Photo of Bander Almutairi
Bander Almutairi
(East Anglia)
Photo of Daniel Buck
Daniel Buck
(East Anglia)
Photo of John Calabrese
John Calabrese
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Jack Campbell
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Thomas Cottrell
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Alastair Darby
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Shabieh Farwa
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Nadia Gheith
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Syed Ghufran
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Adrian Hemery
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Graham Kemp
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Robert Kurinczuk
(East Anglia)
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Antony Lee
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Aoife McMonagle
Photo of Nazar MIHEISI
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Heather Riley
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Veronika Schreiber
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Martin Sell
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Claire Shelly
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Conor Smyth
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Luke Stanbra
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Benjamin Summers
(East Anglia)
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Scott Thomson
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Lewis Topley
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Ramon Vera


Algebraic topologyHatcher
A bestiary of spaces and spectraStrickland
A concise course in algebraic topologyMay


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No assignments have been set for this course.

Recorded Lectures

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