I have a decent background in differential geometry. I have read John Lee's introduction to smooth manifolds and doCarmo's Riemannian Geometry. I was trying to read Misha Gromov's Metric structures for Riemannian and non Riemannian spaces but am finding it extremely difficult to follow. Any suggestions for books/papers as prerequisites ?
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Slightly more advanced books on Riemannian geometry can help, in particular Petersen, and Gallot-Hulin-Lafontaine. Gromov draws a lot of his examples from Riemannian geometry !
Reading Burago-Burago-Ivanov "Introduction to metric geometry" is a also a good idea. It will give the necessary understanding of intrinsic metric spaces.
With this a good part of the book should be understandable.
answered Jan 25, 2014 at 8:09
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9$\begingroup$ I would say "some parts of the book" instead of "good part": Even if you have all the background in the world, reading Gromov's books usually not easy (but very rewarding!). Consider the story of Exercise number 1 from Gromov-Ballmann-Schroeder, which became an infamous open problem (and stayed so until very recently!). $\endgroup$– MishaCommented Jan 25, 2014 at 9:53
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2$\begingroup$ @Misha: I hadn't heard that this exercise had been solved. Can you point me in the right direction? I spent some weeks as a grad student feeling quite dumb for being unable to solve it. ;) $\endgroup$ Commented Jan 25, 2014 at 16:05
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3$\begingroup$ @TomChurch - See here : arxiv.org/abs/1312.2198 $\endgroup$ Commented Jan 26, 2014 at 3:33
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1$\begingroup$ Yes, a "good part" is probably really optimistic ! $\endgroup$ Commented Jan 27, 2014 at 14:46
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$\begingroup$ @ThomasRichard among Petersen and GHL, which would you recommend for self study ? $\endgroup$ Commented Jan 27, 2014 at 20:02