I have some problems with homotopies. The situation is this: Let $X$ be a surface, which is homeomorphic to a 2-Sphere with a finite number (at least 3) of points removed (equivalently, an open ...
I asked this on math.stackexchange.com, but didn't get a single answer. Charles Weibel writes in his survey of homological algebra Riemann defined a surface $S$ to be $(n + 1)$-fold connected ...
A surface is simply a 2-manifold. The classification theorem for compact connected surfaces (with boundary) is commonly regarded in the categories TOP, DIFF and PL. Well known proofs (e.g. via ...
I'm looking for a detailed reference about connected sums. I'd like it to contain a proof that a connected sum of connected surfaces is independent - up to homeomorphism - of the various choices ...
Let me first state the definitions : A not-nullhomotopic closed curve / loop $c$ on an orientable surface $X,c:[0,1]\to X$ is called simple closed curve is $c|[0,1)$ is injective and [ $c(0)=c(1) ] ...
Given an element in the (first) homology group of a surface, I would like to know if it can be represented as a simple closed curve. For orientable surfaces, this is well-known, but I wasn't able to ...