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I know there are text books of Algebraic topology. There are books of Differential geometry. But when I read papers, for example lots of papers talking about fundamental groups or higher homotopy groups of certain manifolds, sometimes lots of terminologies from abstract algebra pop out - nilpoentnilpotent, solvable or amendable amenable etc. I can understand those definitions, but I fell feel very uncomfortable that I don't have a geometric feeling of those languages. So I ask for a good reference, if ideally written by geometerthat will be best, that covers the material of this part?

Thanks in advance for any suggestions.

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I know there are text books of Algebraic topology. There are books of Differential geometry. But when I read papers, for example lots of papers talking about fundamental groups or higher homotopy groups of certain manifolds, sometimes lots of terminologies from abstract algebra pop out - nilpoent, solvable or amendable etc. I can understand those definitions, but I fell very uncomfortable that I don't have a geometric feeling of those languages. So I ask for a good reference, if written by geometer that will be best, covers the material of this part?

Thanks in advance for any suggestions.

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Any text book or lecture notes regarding the algebraic part of geometry?

I know there are text books of Algebraic topology. There are books of Differential geometry. But when I read papers, for example lots of papers talking about fundamental groups or higher homotopy groups of certain manifolds, sometimes lots of terminologies from abstract algebra pop out - nilpoent, solvable or amendable etc. I can understand those definitions, but I fell very uncomfortable that I don't have a geometric feeling of those languages. So I ask for a good reference, if written by geometer that will best, covers the material of this part?

Thanks in advance for any suggestions.