I’m currently reading Burago, Burago, Ivanov’s book A Course in Metric Geometry. I’m really enjoying it so far - what would be a good continuation to the book once I’m done?
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$\begingroup$ Hi! What's your background? $\endgroup$– Dante GrevinoCommented Jun 5, 2019 at 18:41
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$\begingroup$ Hi! I’ve studied analysis from Stein and Shakarchi book 3 and 4. Also some riemannian geometry from Lee and a bit of geometric measure theory. I’ve also read Clara Loh’s book on geometric group theory, which seems to be quite related to this topic. $\endgroup$– James BaxterCommented Jun 5, 2019 at 18:53
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$\begingroup$ That’s all of the relevant background I can think of for now.. $\endgroup$– James BaxterCommented Jun 5, 2019 at 18:53
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3$\begingroup$ see arxiv.org/abs/1903.08539. $\endgroup$– Igor BelegradekCommented Jun 6, 2019 at 10:30
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1 Answer
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As you have been reading Loh's book, I recommend you take a look at Metric spaces of non-positive curvature by M. Bridson and A. Häfliger.
See also An invitation to Alexandrov geometry: CAT(0) spaces by S. Alexander, V. Kapovitch and A. Petrunin, or its older version.
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$\begingroup$ @AntonPetrunin Hi, I took a look to your notes and I think they are a very good introduction. Since they were already mentioned in another comment, I have added them to my answer to make them easier to find. $\endgroup$ Commented May 11, 2020 at 8:24
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$\begingroup$ The book mentioned by Igor Belegradek is a bigger project, so far only draft is available; it is more like reference source (not an introduction). $\endgroup$ Commented May 11, 2020 at 18:07
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$\begingroup$ @AntonPetrunin I see, it is good to know! $\endgroup$ Commented May 23, 2020 at 6:31
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1$\begingroup$ @GabrielRomon I think your are talking about different books both versions of "Invitation" anton-petrunin.github.io/invitation are nearly identical and the big book arxiv.org/abs/1903.08539 is not finished. $\endgroup$ Commented Jun 19, 2020 at 4:11