MAT 530 or its contents (basic
and covering spaces)
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:
- An elegant and clear definition of cell complex
- The distinction between regular cell complexes and general cell complexes (the CW complexes of J.H.C. Whitehead)
- Homology groups of regular cell complexes
- The invariance theorem depending on the functorial aspects of regular cell complex homology
- Singular homology (in the more geometric variant of Steenrod)
- Introductory homotopy theory
- Skeletal homology for general cell complexes.
||moira at math.sunysb.edu
||3-119 Math Tower
||dennis at math.sunysb.edu
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