a bound depending on the Heegaard Floer homology of $Y$. Indeed, $$\label{Nestimate1}
N_Y = {1\over 2}(\dim_{{{\mathbb F}}} \widehat{HF}(Y) - |\mathrm{Tor}\ H_1(Y; {\mathbb{Z}})|)$$ suffices for the Theorems \[thm1\] and \[thm2\] above, where $\widehat{HF}(Y)$ denotes the Heegaard Floer groups of $Y$ with coefficients in ${{\mathbb F}}={{\mathbb Z}}/2{{\mathbb Z}}$ and $|\mathrm{Tor}\ H_1(Y; {\mathbb{Z}})|$ is the number of elements in the torsion submodule of first singular homology. Theorem \[thm2\] can be viewed as an answer to [[Ozsváth and Szabó]{}]{}’s question, and Theorem \[thm1\] as a geometric interpretation of the rank of the Heegaard Floer homology groups of a $3$-manifold $Y$: it is a “speed limit" for fibered knots in $Y$ with respect to the twist coefficient. Such an interpretation raises the natural question

\[question2\] Does every $3$-manifold contain a “fast" knot? That is, a fibered knot for which the absolute value of the twist coefficient lies in the interval $[N_Y,N_Y+1]$?

This question is closely tied to the conjecture that L-spaces are exactly those 3-manifolds without taut foliations. Indeed, an affirmative answer to Question \[question2\] would imply this conjecture, by recent work of Kazez and Roberts [@kazezrobertsII]. In a related direction, is perhaps worth pointing out the following corollary, stated in terms of the [*reduced*]{} 