Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on the geography problem in Heegaard Floer homology   We give new obstructions to the module structures arising in Heegaard Floer
homology. As a corollary, we characterize the possible modules arising as the
Heegaard Floer homology of an integer homology sphere with one-dimensional
reduced Floer homology. Up to absolute grading shifts, there are only two. We
use this corollary to show that the chain complex depicted by Ozsv\'ath,
Stipsicz, and Szab\'o to argue that there is no algebraic obstruction to the
existence of knots with trivial $\epsilon$ invariant and non-trivial $\Upsilon$
invariant cannot be realized as the knot Floer complex of a knot.

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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph