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Stony Brook MAT 539
Algebraic Topology
  Fall 2012

MAT 539 Algebraic Topology

Stony Brook University - Fall 2010



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

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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