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 now 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 geo needed in physics in sufficient detail, but not too mathematical? I heard some names such as Nakhara, fecko, spivak. How are these?