Cedar Turek

Thesis Advisor: Dr. Haydee Lindo (Harvey Mudd College - Department of Mathematics)

Second Reader: Dr. Francis Su (Harvey Mudd College - Department of Mathematics)

Contact: cturek@hmc.edu

A Gentle Introduction to Differential Topology

The original motivation for this thesis was to learn enough differential topology prove the Generalized Stokes Theorem, but I quickly discovered that differential topology is quite hard to understand through reading alone. I aim to change that by providing a more in-depth discussion of the fundamental topics, exhibiting tangible examples, and working through relevant problems. 

We define key terms, such as manifolds, parametrizations, immersions, submersions, embeddings, transversality, and homotopy. Additionally, we state and prove some key theorems, including the local immersion and submersion theorems, the preimage theorem, and a stability theorem. Appendix A contains several relevant problems with solutions.