Manifolds II: Differential Forms , Winter, 2021. (Jan 5 -Mar 11).

meets: MWF 11:40 to 1:10 via Zoom
SYLLABUS might be here, eventually

Reading & HW assignments; Presentations, by week

HWs (includes GP exercises)

Main References
Guillemin and Pollack Differentials Topology (Chapter 4)
Flanders Differentials Form with Applications..
Sjamaar

copies of class lectures here

HW Solutions & Class Presentations
solutions
presentations

Additional References
Exterior Differential Systems Bryant et al (MSRI library)
rmont's book review w picture of contact distrib.
Burke Div, Grad, Curl are Dead
Abr-Mars forms from Found. of Mech. ; see esp table 2.4.1, p. 121.
Lie group coho notes
Cartan's book (poorly translated to English) and review of same

Mechanics; Geodesics
rigid bodies (T Tao's answer)
video of tennis racket/ Dzhanibeko
rigid bodies, fluids Rajeev
also see: Arnol'd p 133, or Abraham-Marsden (consult index), or ch 15 of Marsden and Ratiu's "Intro. to Mechanics and Symmetry"


some wikis:
differential forms
differential geometry of surfaces
vector bundles