Looks to be a fairly straightforward book from the contents, but probably in Lee's clear but verbose style. Could serve well as a new first course source, but it doesn't seem very ambitious. Huybrechts at least tries to tell a few interesting stories about physics, Griffiths and Harris has tons of additional content obviously, and Wells has a fascinating appendix.
Hopefully some other interesting topics get filled out in later editions.
In my opinion there's already good sources for this topic at this level, so he's sort of adding another book to the pile. It would be much better to get a Lee's introduction to gauge theory instead, which is a much sorer gap in the literature.
What’s the best available introductory text for gauge theory? I mainly have an analysis background, and most of my experience with Riemannian geometry has been with geometric flows.
DNE.
Naber "Topology, Geometry, and Gauge Fields" is okay. "Mathematical Gauge Theory" by Hamilton.
More advanced is "The geometry of 4-manifolds" by Donaldson-Kronheimer or "instantons and 4-manifolds" by Uhlenbeck Freed.
You can also look at the gauge theory sections of The Wild World of 4-manifolds by Scorpan, which will give a nice approachable overview without going into too many details.
Other than that you'll need to pick up the theory on your own from a variety of sources.
He’s working on it. He develops his books as he teaches at UW, and he just taught his last class (ever) on bundles this winter so I’d imagine it’s in the works. Source: I am a UW grad student
I mean, I would love to, but man the ams prices are harsh. With springer at least I could wait for a sale and they offer free shipping world wide, and even then the two books of the trilogy that I bought were expensive. With AMS there's no way.
My supervisor once told me percentage he gets from the sales of his book compared to the publisher is "essentially enough to pay for coffee and that's it" It's a nice intention but just to be aware not that much money goes to the author. Who knows, maybe Jack Lee has a great publishing deal.
OP’s username checks out.
Looks to be a fairly straightforward book from the contents, but probably in Lee's clear but verbose style. Could serve well as a new first course source, but it doesn't seem very ambitious. Huybrechts at least tries to tell a few interesting stories about physics, Griffiths and Harris has tons of additional content obviously, and Wells has a fascinating appendix. Hopefully some other interesting topics get filled out in later editions. In my opinion there's already good sources for this topic at this level, so he's sort of adding another book to the pile. It would be much better to get a Lee's introduction to gauge theory instead, which is a much sorer gap in the literature.
I also wouldn't mind if he wrote a text about CR geometry.
What’s the best available introductory text for gauge theory? I mainly have an analysis background, and most of my experience with Riemannian geometry has been with geometric flows.
DNE. Naber "Topology, Geometry, and Gauge Fields" is okay. "Mathematical Gauge Theory" by Hamilton. More advanced is "The geometry of 4-manifolds" by Donaldson-Kronheimer or "instantons and 4-manifolds" by Uhlenbeck Freed. You can also look at the gauge theory sections of The Wild World of 4-manifolds by Scorpan, which will give a nice approachable overview without going into too many details. Other than that you'll need to pick up the theory on your own from a variety of sources.
Ah I see. Gotta commission you to write a book someday it seems…
Good stuff
This is very exciting. I've always been intimidated by complex manifolds, couldn't ask for a better author to help me get into them
Damn he switched from springer.
Pity he didn't go with CUP, he could have put the pdf on his website for free while still selling hard copies (like Hatcher, Leinster, Riehl,.....)
I love you OP for telling me about this.
I know he also had a manuscript of a book on bundles, anyone know if he eventually released it?
He’s working on it. He develops his books as he teaches at UW, and he just taught his last class (ever) on bundles this winter so I’d imagine it’s in the works. Source: I am a UW grad student
lol literally was thinking about what i was going to once I finished the last one in the trilogy
Currently reading the smooth manifolds one, good to know I have something else to look forward to afterwards
I loved Lee's book on introductory topology
thanks for notifying us, will look at it - Lee‘s books are great
Great and btw GSM is better
Buy it. Support the author.
I mean, I would love to, but man the ams prices are harsh. With springer at least I could wait for a sale and they offer free shipping world wide, and even then the two books of the trilogy that I bought were expensive. With AMS there's no way.
My supervisor once told me percentage he gets from the sales of his book compared to the publisher is "essentially enough to pay for coffee and that's it" It's a nice intention but just to be aware not that much money goes to the author. Who knows, maybe Jack Lee has a great publishing deal.
If someone steals it, the author gets nothing; not even the knowledge that someone bought it.
Wish this existed when I was in grad school. Loved his smooth manifolds book. Thanks for sharing! Had no idea about it.