Introduction to the Geometry of Foliation, Part B: by Dr. Gilbert Hector, Dr. Ulrich Hirsch (auth.)

By Dr. Gilbert Hector, Dr. Ulrich Hirsch (auth.)

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Additional info for Introduction to the Geometry of Foliation, Part B: Foliations of Codimension One

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SI. 2. ytic. d bundle. ptionai. mtrUmai. ~ u. Following Raymond's thesis [Ra] we construct an analytic foliation of codimension one with an exceptional minimal set. 1 the manifold will be B x SI and the foliation is obtained by suspending a Fuchsian group In part developed for the construction of a COO C this example will be further foliation on S3 (or any odd- dimensional sphere) with an arbitrary finite number of exceptional mini-mal sets. We remark that Raymond's example is closely related to Sacksteder's example of a COO foliation on B x SI with an exceptional minimal set.

Then W by t1 - c~ is a .... ~(p) A(x) I = for x E M - W. p(x) 1/2 o A extends Figure II a) Show that the I-form w' extends by on AW + (I-A)dp W on is without singularities and M- W, int~ grable. Let We suppose that F more we assume that w o wlB such that given by w' is obtained by 8. T~buliz~ng (M,F) F' along a Cr be a bound~y component. is transverse to the boundary component F W = B x [0,1) is isomorphic to and that B. Further- is given by a I-form w with the property that is closed. 1 there is a collar neighbourhood Flw 2 ~ r ~ ~.

1 constitutes a product except possibly in dimension four where it is still unknown at the time of writing this whether or not any orientation preserving homeomorphism of m4 is isotopic to the identity. - intersects every leaf of Call a closed transversal of F total if it F. Show that every closed transversal of a Denjoy foliation on T2 is total. 5. Z. omponent. 5 foliation R on 51 x Sm-I. We think of components and choose a transverse the restrictions of Rand COO the construction of the Reeb R as the union of two Reeb foliation of Rm to some open neighbourhood R such that W of the - 50 core of each of these components form a product.

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