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Time: TTh 12:00-1:15
Room: Math 215
Textbook: Algebraic Topology by Allen Hatcher
The plan is to cover Chapter 2 and most of Chapter 3
Instructor: Jeremy Miller
Instructor's email: jeremykmiller at purdue dot edu
Instructor's office hours: 10:30-11:45 on Tuesday and by appointment
Instructor's office: Math 710
Grade distribution:
Homework 100%
Homework:
Homework 1, due January 21st
Section 2.1: 11, 12
Homework 2, due January 28th
Section 2.1: 16, 18
Also write up a complete proof of homotopy invariance of homology.
Homework 3, due February 4th
Section 2.1: 17 and Section 2.2: 1,6
Also prove the following: Let U be an open cover of X. Prove that the inclusion of C*U(C) into C(X)* is a chain homotopy equivalence.
Homework 4, due February 11th
Section 2.1: 20, 22 and Section 2.2: 2
Homework 5, due February 18th
Section 2.2: 3,7,13
Also prove that the kernel of the natural map from the fundamental group to the first homology group is the commutator subgroup.
Homework 6, due February 25th
Section 2.2: 28, 43
Section 3.A: 2, 6
Homework 7, due March 3rd
Section 2.2: 40
Section 2.B: 1,6
Also describe how maps of modules induce maps on Tor. Moreover do this in a "reasonable" way. For example, do not just say they induce the zero map.
Homework 8, due March 10th
Section 1.2: 22b (try to do this without using part a)
Section 2.C: 1,2,4
Homework 9, due March 24th
Section 3.1: 1,2,3,4
Also show every divisible module over a PID is injective.
Homework 10, due March 31st
Section 3.2: 1,3a,4,5
Homework 11, due April 7th
Section 3.2: 2,7,10,11
Homework 12, due April 14th
Section 3.2: 14 (ignore the part of the question starting with the word "next"), 15
Also prove that the long line is not paracompact.
Homework 13, due April 21th
Section 3.3: 2,5,11,12
Homework 14, due April 28th
Section 3.3: 20, 25, 30
Links:
-Notes on Tor and Ext by Peter May
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