# Tagged Questions

547 views

### Space of embeddings of circle in a surface

Let $S$ be a compact oriented surface of genus at least $2$ (possibly with boundary). Let $X$ be a connected component of the space of embeddings of $S^1$ into $S$. Question : what is the ...
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### Explicit computation of the action of a Dehn twist on the fundamental group of a surface

Let $S$ be a compact orientable surface of genus $g$. Now let $p\in S$ and $\gamma$ a closed simple curve on $S$ disjoint from $p$. It is not very difficult to compute the action of a Dehn twist along ...
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### Homotopy versus path-homotopy on punctured surface

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 ...
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### Looking for software that computes intersection numbers (Heegaard Diagrams)

As a part of my research I am working with intersection matrices of Heegaard diagrams. Is there some software that could help me compute such matrices for some examples? Thanks.
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### Dimension of the homology group with coefficients in $\mathbb{Z}/2\mathbb{Z}$

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 ...
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### Classification of surfaces and the TOP, DIFF and PL categories for manifolds

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 ...
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### Connected sum of surfaces

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) ] ...