I am blown away by exposition of analytic manifolds in Serre's Lie algebras and Lie groups, I want more! Is there a text that treats classic topics of differential geometry like connections, Riemannian metrics, holonomy, de Rham cohomology, (almost) complex manifolds, homogeneous spaces, symmetric spaces in such a manner? Or maybe some more analytic manifolds, towards the modern research topics?
Differential geometry text with categorial flavor
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0Oops. I should have clicked that link before commenting. I guess that is basically what the old post was about. – 2011-09-30