MAT 539 Algebraic Topology

Homework

Week starts	Sections	HW #	Assignements-
8/27	Chapter 1 Complexes	1	Pag. 4, exercises 4 and 6. Pag. 19, ex 1 and 3. Describe all possible complexes on the open interval (0, 1), on (0, 1] and on [0, 1]. Give an example of a connected topological space which cannot be given the structure of a complex.
9/3		2
9/10		3
9/17		4
9/24		5
10/1		6
10/8		7
10/15		8
10/22		9
10/29		10
11/5		11
11/12		12
11/19
11/26		13
12/3		14
12/10
12/17

Prerequisite

MAT 530 or its contents (basic topology, fundamental group and covering spaces)

Textbook

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.

Topics

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.

Instructors 

	email	Office
Moira Chas	moira at math.sunysb.edu	3-119 Math Tower	Mo 10-12 (3-119) Fr 11-12 (P-143)

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