## Confoliations.(English)Zbl 0893.53001

University Lecture Series. 13. Providence, RI: American Mathematical Society (AMS). ix, 66 p. (1998).
A transversely oriented plane field $$\xi$$ on an oriented 3-manifold can be defined as the kernel of some nowhere vanishing 1-form $$\alpha$$. $$\xi$$ is called a confoliation if either $$\alpha \wedge d \alpha \geq 0$$ or $$\alpha \wedge d \alpha \leq 0$$. Thus confoliations provide a link between codimension 1 foliations (the case $$\alpha \wedge d \alpha \equiv 0$$) and contact structures (the case that $$\alpha \wedge d \alpha$$ never vanishes).
This monograph develops the foundations of confoliations on 3-manifolds. The authors prove that $$C^2$$-taut foliations can be $$C^0$$-perturbed into a tight contact structure.
The concept of a confoliation, without the name, first appeared in the work of S. J. Altschuler [Ill. J. Math 39, 98-118 (1995; Zbl 0809.53030)].
Reviewer: J.Hebda (St.Louis)

### MSC:

 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry 57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 57N10 Topology of general $$3$$-manifolds (MSC2010) 53C12 Foliations (differential geometric aspects) 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R30 Foliations in differential topology; geometric theory

### Keywords:

confoliation; contact structure; foliation; 3-manifold

Zbl 0809.53030