# Ozsvath-Szabo Tau-Invariant

The Ozsvath-Szabo Tau-Invariant was defined in [4]. It satisfies the inequality |tau(K)| ≤ genus_{4}(K).

Heegaard-Floer homology groups were shown to be algorithmic in [2]. This paper works with Z/2Z coefficients.

In [3], the authors resolve orientation issues and give an algorithm for computing Heegaard Floer knot and link
invariants using Z coefficients. They also give a combinatorial proof that these invariants are well defined.

## Specific Knots

Baldwin and Gillam have used this combinatorial approach to compute the
Heegaard-Floer homology of many knots, including 11 crossing non-alternating knots [1].
In particular, they show tau(10_{141}) = 0.

## References

[1] Baldwin, J. and Gillam, W. D., "Computations of Heegaard-Floer knot homology,"
Arxiv preprint.

[2] Manolescu, C., Ozsváth, P., and Sarkar, S., "A combinatorial description of knot Floer homology."
Arxiv preprint.

[3] Manolescu, C., Ozsváth, P., Szabó, Z., and Thurston, D., "On combinatorial link Floer homology,"
Arxiv preprint

[4] Ozsváth, P. and Szabó, Z., *Knot Floer homology and the four-ball genus*, Geom. Topol. **7**
(2003), 615-639.