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Is there any known algorithm for computing the Heegard-Floer homology of a given 3-manifold from a Heegard diagram?

I am trying to compute it from the definition, and most of the steps can be put in an algorithmic way (in the sense that they can be programmed into a computer, for example), but at some point you need to count points in a moduli space of a homotopy class (which is not even uniquely determined). I really see no way to automatically compute this.

Is there any purelly combinatorial way to compute these groups?

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Yes, and this is documented by easily-findable literature, starting with a paper by Sarkar-Wang. Voting to close. – Tim Perutz Dec 10 '12 at 18:22
It's not at all clear to me why this question should be closed. Many MO questions have brief answers of the form "See paper X". Do people think that all questions of this type should be closed? If not, what's different about this one? – Kevin Walker Dec 10 '12 at 20:52
Kevin: for me, the point is that in this case the information is easily retrievable using a Google search (Sarkar-Wang's arxiv submission is currently the first hit in a search for "algorithm heegaard floer") and the question can be answered completely by MathSciNet search. To keep the quality of MO high, I think that questioners should be expected to do some basic checks before asking. Sometimes, searching for guessable keywords does not lead to the relevant literature, and in such cases it's useful to have an expert point in the right direction – Tim Perutz Dec 10 '12 at 21:11
Tim: Thanks for the response. I agree that ideally people should do the obvious Google searches before asking on MO. But I also think that keeping MO a friendly place is worthwhile, and voting to close (as opposed to gently reminding the new user that the answer is easy to find via google) strikes me as a little bit unfriendly. I think reasonable people can disagree about where to draw the line on too-obvious/too-googlable/etc, and for this reason one should give others the benefit of the doubt. (Just to clarify, I'm only advocating friendliness toward... – Kevin Walker Dec 10 '12 at 21:39
It would be wiser to err on the side of inclusiveness in MO. At its best it is a very useful summary of the mathematical literature, indeed especially of facts that are in some sense "easily findable". – Greg Kuperberg Dec 11 '12 at 3:36

Tim Perutz answered the question in the comments: Yes, there is a combinatorial algorithm; see the paper of Sarkar and Wang.

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