The tangent bundle of a vector bundle and my recommendation for a thorough Differential Geometry book

cf. Peter Michor "Topics on Differential Geometry" Sec. 8.12
cf. Peter Michor “Topics on Differential Geometry” Sec. 8.12

I’m trying to tackle the following topics in Peter Michor’s Topics on Differential Geometry, a book that I highly recommend because if you want a comprehensive, thorough, almost encyclopedia-like, and rigorous reference or even textbook on Differential Geometry, this is it. Even the choice of notation by Michor is well-designed and rational.

The book is massive but his treatment is so good, I’m willing to invest a lot of my time and effort into trying to work through the book.

I’m working through Sec. 8.12-8.13 for a tangent bundle of a vector bundle. It’s the big boy version of a second derivative. Then I want to get to the Geometry of Geodesics and geodesic structure. It’s slow but insightful slogging.

I throw up all my very raw notes into a laTeX that I call a dump file. I was listening to David DeAngelo speak on his advice for learning a new skill or topic, referring to Clark Terry, a jazz trumpet player. Terry says to “Imitate, Assimilate, Innovate.”

Imitate the best. -David DeAngelo

Imitate, Assimilate, Innovate. -Clark Terry

So a lot of times, I’m imitating and copying in my notes, as I try to assimilate what’s going on (and most of the time, I don’t know what’s going on). My notes are my struggle with trying to learn this stuff and I’m not a very smart guy. But I’m putting it out there.

I’m not going to drain much of my effort into typing up my notes into html’s version of LaTeX as I’ve found the process not effective in terms of time and effort spent, so what I’ll do is take a jpg of the most important or interesting stuff and provide a full pdf and LaTeX file, always open, available, and public, on my Google Drive.

Thanks for reading and have a great week and I’ll keep trying to put out more good stuff as I keep learning.


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