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I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know. I know some basic concepts reading from the Internet on topological spaces, connectedness, compactness, metric, quotient Hausdorff spaces. Do I need to go deeper? Also, could you suggest me some chapters from topology textbooks to brush up this knowledge. Could you please also suggest a good differential geometry books that covers diff. geom. needed in physics in sufficient detail, but not too mathematical? I heard some names such as Nakahara, Fecko, Spivak. How are these?