Point-Set Topology (MSU - Fall 2006 - Futer)

 

Homework 1: the basics (Gemignani 1.1 - 2.3)

 

Homework 2: metric spaces and continuity (Gemignani 2.4 - 2.7)

 

Homework 3: topologies on sets (Gemignani 3.1 - 3.3)

 

Homework 4: derived sets and subspace topology (Gemignani 3.4 - 4.1)

 

Homework 5: continuous functions and homeomorphisms (Gemignani 4.3 - 4.6)

 

Homework 6: quotient spaces and Hausdorff spaces (Gemignani 4.5, 5.2)

 

Homework 7: manifolds and open covers (Gemignani 7.1 - 7.3)

 

Homework 8: compactness (Gemignani 7.3 - 7.4)

 

Homework 9: local compactness and compactifications (Gemignani 8.1 - 8.3)

 

Homework 10: sequential compactness, completeness (Gemignani 8.4 - 9.1)

 

Homework 11: connectedness and compactification (Gemignani 9.1 - 9.3)

 

Homework 12: path, local, and regular connectedness (Gemignani 9.3 - 9.4)

 

 

Algebraic Topology (MSU - Spring 2007 - Futer)

 

Homework 2: Borsuk-Ulam and retractions (Hatcher 1.1)

 

Homework 3: fundamental group and van Kampen (Hatcher 1.1-1.2)

 

Homework 4: quotient spaces and fundamental group (Hatcher 1.2)

 

Homework 5: covering maps (Hatcher 1.3)

 

Homework 6: covering spaces (Hatcher 1.3)

 

Homework 7: covering space actions and fundamental group (Hatcher 1.A-1.B)

 

Homework 8: delta complexes and simplicial homology (Hatcher 2.1)

 

Homework 9: simplices and retractions (Hatcher 2.1)

 

Homework 10: homology (Hatcher 2.1)

 

Homework 11: homology with Mayer-Vietoris (Hatcher 2.1 - 2.2)

 

 

 

Differential Topology (MSU - Fall 2007 - Parker)

 

Homework 1: diffeomorphisms and charts (Lee Ch 1 - 2)

 

Homework 2: tangent spaces and pushforwards (Lee Ch 3 - 4)

 

Homework 3: vector fields and Lie brackets (Lee Ch 4, 18)

 

Homework 4: immersions, embeddings, and the preimage thm (Lee Ch 7 - 8)

 

Homework 5: Lie groups, specifically, orthogonal and unitary groups (Lee Ch 9)

 

Homework 6: distributions, double-duals, and df (Lee Ch 19, 6)

 

Homework 7: differential forms and integrals on curves (Lee Ch 14)

 

Homework 8: vector spaces and covectors (Lee Ch 11 - 12)

 

Homework 9: pullback, pushforward, symplectic forms (Lee Ch 12)

 

Homework 10: orientation forms and Stokes’ thm (Lee Ch 13 - 14)

 

Homework 11: De Rham cohomology (Lee Ch 15)

 

Homework 12: Riemannian manifolds and gradients (Lee Ch 11)

 

 

 

Differential Geometry (MSU - Spring 2008 - Roberts)

 

An Introduction to Distributions and Foliations

 

The Hopf Degree Theorem, written by guest contributor Chris Zin