Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot Floer homology and the four-ball genus   We use the knot filtration on the Heegaard Floer complex to define an integer
invariant tau(K) for knots. Like the classical signature, this invariant gives
a homomorphism from the knot concordance group to Z. As such, it gives lower
bounds for the slice genus (and hence also the unknotting number) of a knot;
but unlike the signature, tau gives sharp bounds on the four-ball genera of
torus knots. As another illustration, we calculate the invariant for several
ten-crossing knots.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph