Math 5520: Intro to Topology II


Instructor: Mladen Bestvina
Office: JWB 210
Office hours: after class or by appointment
Text: James Munkres Topology, 2nd ed
Meets: MWF 9:40-10:30 in LCB 215
Midterms: Feb 11, March 25
Final: April 25, 8-10 am.

There are two second editions of the book available, the older version from Prentice Hall and the new one, from Pearson. The differences are small and either version will work for the class (the Pearson version omits the last chapter and reverses the previous two). We will cover the last part of the book, about the fundamental group, covering spaces and classification of surfaces. There will be additional topics based on handouts.

The grade will be based on homework, midterms, final, and class activity.


Homework 1, due Jan 18:
§ 51: 1,3, § 52: 2,3,6

In § 52 problems, note that the book uses the "hat" notation for the homomorphism induced by a path, while in class I used the "star" notation.


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Homework 2, due Feb 1:
§ 53: 3,4, § 54: 8, § 55: 2, § 56: 2. Extra credit: § 57: 3.

In addition, on Wednesday Jan 30 we'll have a problem session. Please prepare a problem or two to present in class from sections 51-57 not assigned for homework.

Homework 3, due Feb 22:
58.2, 59.1, 60.5 and this exercise on free groups. On 58.2 include descriptions of deformation retractions (you don't have to give explicit formulas).

In addition, there is extra credit on the ping-pong lemma.


Homework 4, due March 8.

In addition, on March 6 we'll have a problem session. Prepare to present a problem from sections 58-60 and 67-73 not assigned for homework.

Homework 5, due April 5:

77.1, 77.3 d,e,h (for these carry out the cut and paste procedure to put them in standard form),

77.3 a,b,c,f,g -- decide which surface it is by computing Euler characteristic and orientability.

In addition, compute the fundamental group of the space obtained from the torus by identifying 3 distinct points.

Extra credit: 77.4 (hint: Euler characteristic)


Until the end of the semester we will be studying free groups in more detail, using these notes.

Here is the folding cheat sheet.

Homework 6 due April 19.