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In this paper, we study topological numbers for uncharged and charged staticblack holes obtained in Ho\v{r}ava-Lifshitz gravity theory in differentensembles. We first calculate the topological numbers for the uncharged blackholes by changing the value of the dynamic coupling constant, and find that theblack holes with spherical and flat horizons have the same topological number.When the black hole's horizon is hyperbolic, different values of the couplingconstant generate different topological numbers, which can be $1$, $0$ or $-1$.This shows that the coupling constant plays an important role in thetopological classification. Then, we study the topological numbers for thecharged black holes in different ensembles. The black hole with a sphericalhorizon has the same topological number in canonical and grand canonicalensembles. When the horizons are flat or hyperbolic, they have differenttopological numbers in canonical and grand canonical ensembles. Therefore, thetopological numbers for the uncharged black holes are parameter dependent, andthose for the charged black holes are ensemble dependent.

Topology of Ho\v{r}ava-Lifshitz black holes in different ensembles