I. Nikolaev - 3-manifolds, foliations and

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I. Nikolaev - 3-manifolds, foliations and $K_0\bigl(C(X)\rtimes Z\bigr)$

I. NIKOLAEV, CRM, Université de Montréal, Montréal, Québec H3C 3J7, Canada

3-manifolds, foliations and $K_0\bigl(C(X)\rtimes Z\bigr)$

J. F. Plante [1] classified 3-dimensional manifolds M such that every foliation ${\cal F}$ on M has a compact leaf. Plante's method is based on estimation of `growth rate' of the fundamental group $\pi_1(M)$ .

We show that calculation of a `dimension function' of K₀-group of the crossed product $C^\ast$ -algebra generated by ${\cal F}$ leads to series of results covering Plante's classification.

References

1. J. F. Plante, Foliations with measure preserving holonomy. Ann. of Math. 102(1975), 327-361.