411 Class Summary

Math 411 Class Summary

Week 1

Monday. Introduction. First examples.
Wednesday. Projective space. Definition of a manifold.
Friday. Mappings.

Reading:

J.P. May's quick introduction to topology (see handouts link), sections 1 and 2.
Read our text, sections 1.1 and 1.2.

Homework:

None this week.

Week 2

Monday. Three versions of tangent space.
Wednesday. Tangent space, continued.
Friday. Tangent space, continued. Tangent mapping.

Reading:

Chapter 2.

HW 1 due Friday, February 8:

HW 1

Please latex your homework solutions. Hand-drawn figures are OK (use '\vskip 1in' or something like that to make room). Here are two possible templates:

There is a place to fill in your name at the top of each template. In the plain template, you may want to uncomment

%\usepackage{fullpage}

(i.e., remove the '%') near the top of the document. This will make the margins smaller. I am happy to receive a pdf of your HW by email rather than a hardcopy.

Week 3

Monday. Products, coproducts, tensor products.
Wednesday. Tensor and exterior products.
Friday. Exterior and symmetric products. Dual space.

HW 2 due Friday, February 15

HW 2, fancy solution template, plain solution template

Week 4

Monday. Duality, pullbacks. Tangent and cotangent bundles.
Wednesday. Differential forms, mappings.
Friday. Differential forms. Orientation.

HW 3 due Friday, February 22

HW 3 (fancy solution template, plain solution template)

Here is a pdf of the fancy solution template. You may want to take a look at the typesetting of the commutative diagram that appears there. I am using the latex package tikz (which is part of the standard tex distribution). For details, please see the tex file (including its preamble). As an alternative, you may want to use \vskip to make room for hand-drawn diagrams in your homework.

Week 5