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General


Description

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

Semester

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

Timetable

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

Prerequisites

Some knowledge of general topology and commutative rings.

Syllabus

  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.

Lecturer


Neil Strickland
Email N.P.Strickland@sheffield.ac.uk
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.


Students


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


Bibliography


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


Note:

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Assessment



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Recorded Lectures


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