Stony Brook MAT 539
Algebraic Topology
  Fall 2011

MAT 539 Algebraic Topology

Stony Brook University - Fall 2010



Textbook: Homology of Cell Complexes

Notes on the course of  Norman Steenrod by George E. Cooke and Ross L. Finney

Princeton University Press; 1st edition (1967)

We like this treatment because it straddles the zone between geometry and algebra and provides a solid basis for understanding algebraic topology.


The sequence of concepts goes as follows:
  1.  An elegant and clear definition of  cell complex
  2. The distinction between regular cell complexes and general cell complexes (the CW complexes of J.H.C. Whitehead)
  3. Homology groups of regular cell complexes
  4. The invariance theorem depending on the functorial aspects of regular cell complex homology
  5. Singular homology (in the more geometric variant of Steenrod)
  6. Introductory homotopy theory
  7. Skeletal homology for general cell complexes.



Moira Chas
moira at
3-119 Math Tower
Dennis Sullivan

dennis at
5th Math Tower

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