Homotopy Theory

Week 1:

Elementary Homotopy Theory

The Category of Pointed Spaces

Pointed Homotopy

Exercises:

The Homotopy Category

Introduction to Lusternik-Schnirelmann Category

Week 2:

The Fundamental Group

Fibrations I

Exercises:

Cofibrations

Week 3:

Fibrations II - The Fundamental Lifting Property

Exercises:

Co-H-Spaces

Week 4:

Fibrations III (Almost There...)

Partitions of Unity

Exercises:

Cofiber Sequences

Week 5:

Exercises:

Pointed and Unpointed Homotopy Sets

Week 6:

Fibrations IV

Exercises:

The Mapping Cylinder

Week 7:

H-Spaces

Exercises:

Cofiber Sequences II

Week 8:

Exercises:

Homotopy Pushouts I

Week 9:

Exercises:

Homotopy Pushouts II

Week 10:

Exercises:

Coactions

Week 11:

Exercises:

The Bott-Samelson Theorem

Notes:

Notes on Point-Set Topology

Paracompact Spaces

The Fundamental Group of a Co-H-Space is Free