The bold red numbers correspond to problems that have to be submitted for grading.

Fundamental Group (Chapter 9)

§51, p.330: 1,2,3

§52, p.334: 1,2,3,4,6,7

§53, p.341: 1,3,4,5

§54, p.347: 1,3,4,5,6,8

§55, p.353: 1,2

§56, p.356: 1,2

§58, p.366: 1,2,3,4,5,6

§59, p.370: 1,2,3,4

§60, p.375: 1,2,4

van Kampen theorem (Hatcher 1.2 and Munkres Chapter 11)

Munkres, §68, p.421: 2

Munkres, §71, p.438: 2,3,5

Hatcher, Section 1.2, p.52: 2,3,4

Munkres, §72, p.441: 1,3

Munkres, §73, p.445: 1,2 (see Exersice 8 in §35 for the definition),3

Classification of Surfaces (Chapter 12)

§74, p.453: 1,2,3,4,5,6,7; Describe presentations of the fundamental groups of a torus with 1 and 2 punctures.

§75, p.457: 1,2,3,4

§76, p.462: 1,2

§77, p.470: 1,2,3,4, Where on the list in the Classification Theorem is the surface P#K#T#S#P#P#T#T#S? (here P - is a projective plane, K - Klein bottle, T - a torus and S - a sphere)

Classification of Covering Spaces (Chapter 13)

Munkres, §79, p.483: 1,2,3,4.

Munkres, §80, p.487: 1.

Munkres, Supplementary Excersices, p.499: 5

Hatcher, Section 1.3, p.79: 4,9,10.

Homology (Hatcher, Chapter 2)

Hatcher, Section 2.1, p.131: 1,2,4,5, Compute simplicial homology groups of a 2-sphere and 3-ball directly.

Updated: April 24th, 2013
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