Brief review of the main aspects of the f(R) theories of Gravity in the metric formalism. Main reference 10.1103/RevModPhys.82.451 and arXiv:0805.1726 [gr-qc].
Talk about the Poincaré Conjecture. The original proof by G. Perelman can be found in arxiv: math/0211159, math/0303109 and math/0307245 as well as a complete demonstration in arXiv:math/0607607 by John W. Morgan and Gang Tian.