Math232A websyllabus

MATH 232A

Algebraic Topology

Instructor

Prof. Martin Scharlemann
Fall 2009
Office: SH 6718
Office hours: TR 9:00-10:30^a.m.
Telephone: 893 4101
Email: mgscharl@math.ucsb.edu

Text

Allen Hatcher, Algebraic Topology

Lectures

MWF 10-10:50 in SH 4607B

Homework

Homework will typically be due Wednesday following the week assigned. Thus, problems 1, 2 on p. 131 are due Wednesday 30 September. Exceptions, mostly due to holidays, are noted in the table. No late homework will be accepted. Do all problems assigned. Not all will be graded. Feel free to work with each other on the problems, but please then write them up on your own.

Grade

Final	50%
Homework	50%

Schedule (tentative)

Dates Topics Reading Homework

9/25 Introduction pp. 97-101 p. 131: # 1-2

9/28-10/2
Extra class T 9/29 @ 10 Δ-complexes & Simplicial Homology;
Singular Homology pp. 102-107. A more rigorous definition of Δ-complex is in the relevant pages of the on-line version p. 131: # 3, 5, 7 + Extra Problem:
Let Δ be an n-simplex. Suppose each edge in Δ is oriented so that the edges of no 2-simplex face of Δ is cyclically oriented. Then there is an ordering of the vertices of Δ that induces the given orientation on each edge.

10/5-6
Extra class T 10/6 @ 10
No class WF Homotopy invariance;
Exact Sequences pp. 108-118 p. 131: #11, 13, 14

10/12-16 Excision pp. 119-126 p. 132: # 16, 20, 22, 26

10/19-23 Naturality; Equivalence; Degree pp. 127-130;134-137 p. 132: # 27, 29
p. 155: #2, 3

10/26-30 Cellular homology pp. 137-146 p. 155: #7, 10, 12

11/2-6
Extra class T 11/3 @ 10
Euler characteristic;
Split exact sequences;
Mayer-Vietoris sequences pp. 146-149 p. 157: #14, 15, 17
Due Monday 11/16, not 11/9

11/9
No Class WF Homology with coefficients
Veteran's Day pp. 149-155 p. 158: #20, 21, 22
Due Friday 11/20, not Wed. 11/18

11/16-20 Connection with π₁;
Classical applications pp. 166-173 p. 158: #26, 27, 29

11/23-25
No Class Friday More classical applications
Thanksgiving pp. 174-177 p. 158: #31, 32, 40

11/30-12/4 Simplicial approximation pp. 178-184 p. 176: #1, 3, 4

Dates	Topics	Reading	Homework

9/25	Introduction	pp. 97-101	p. 131: # 1-2
9/28-10/2 Extra class T 9/29 @ 10	Δ-complexes & Simplicial Homology; Singular Homology	pp. 102-107. A more rigorous definition of Δ-complex is in the relevant pages of the on-line version	p. 131: # 3, 5, 7 + Extra Problem: Let Δ be an n-simplex. Suppose each edge in Δ is oriented so that the edges of no 2-simplex face of Δ is cyclically oriented. Then there is an ordering of the vertices of Δ that induces the given orientation on each edge.
10/5-6 Extra class T 10/6 @ 10 No class WF	Homotopy invariance; Exact Sequences	pp. 108-118	p. 131: #11, 13, 14
10/12-16	Excision	pp. 119-126	p. 132: # 16, 20, 22, 26
10/19-23	Naturality; Equivalence; Degree	pp. 127-130;134-137	p. 132: # 27, 29 p. 155: #2, 3
10/26-30	Cellular homology	pp. 137-146	p. 155: #7, 10, 12
11/2-6 Extra class T 11/3 @ 10	Euler characteristic; Split exact sequences; Mayer-Vietoris sequences	pp. 146-149	p. 157: #14, 15, 17 Due Monday 11/16, not 11/9
11/9 No Class WF	Homology with coefficients Veteran's Day	pp. 149-155	p. 158: #20, 21, 22 Due Friday 11/20, not Wed. 11/18
11/16-20	Connection with π₁; Classical applications	pp. 166-173	p. 158: #26, 27, 29
11/23-25 No Class Friday	More classical applications Thanksgiving	pp. 174-177	p. 158: #31, 32, 40
11/30-12/4	Simplicial approximation	pp. 178-184	p. 176: #1, 3, 4