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Videos

• Homotopy and Homotopy Equivalence (8:23)

• Homotopy Equivalence - Jonny Evans (20:53)

• Desmos Example from Text

• Algebraic Topology - NJ Wildberger

  • The Fundamental Group - Homotopic Paths and Equivalence (43:04)

• Introduction to the fundamental group (35:12)

• Path Lifting Property (10:12)

• Homotopy Lifting (15:42)

• Surfaces and Topology (57:33) Professor R. Flood

• Hamilton, Boole and their Algebras (54:55) Professor R. Flood

• Hopf Fibration Video (2:19)

• What Hopf Fibrations can tell us about crystallization and glass formation (125:18)

• Van Kampen Theorem and Examples (19:13)

• Eversions

  • Turning a Sphere Inside Out Documentary (Nelson L. Max, 1976) (22:57)

  • Outside In (21:24)

  • The Optiverse (8:43)

  • Torus Eversion

  • Smale's Paradox (13:47)

  • Boy's Surface (2:14), How to Draw (10:15)

Class Links

• March 24 Back in the Saddle Again Echo360

• March 26 Homotopy Equivalent Echo360

• March 31 Path Lifting Notes, Echo360

• April 2 Homotopy Lifting Notes, Echo360

• April 7 Euler Characteristic Notes Echo360

• April 14 Euler Numbers and Homotopy Groups Notes Echo360

• April 16 More Homotopy Groups Notes Echo360

• April 21 Hopf Fibration Notes, hopfcircles.m, hopfmap.m, Echo360

• April 23 Induced Homotopy Notes Echo360

• April 28 Sphere Eversions Notes Echo360

Books

• Essential Topology, M. D. Crossley, 2010.

• Introduction to Topology, 2nd Ed., T. W. Gamelin and R. E. Greene, 1999.

• Introduction to Topological Manifolds, 2nd Ed., J. M. Lee, 2011.

• Topology, 2nd Eb., J. R. Munkres

• General Topology, Lipschutz

• The Topological Picturebook, G. Francis

Notes

• First Day Intro to Topology

• https://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf

• Triangulations of the Sphere by Thurston