Volume Preserving Flows With Cyclic Winding Numbers Groups and Without Periodic Orbits on 3-Manifolds
نویسنده
چکیده
means that if and are any two framed closed surfaces in P that intersect transversely, such that \ is (homologous in to) the longitude of and \ is (homologous in to) the meridian of , then the Pontryagin classes of , and form a basis of H 1 (P ;Z). Recalling the construction of M by surgery in T 3 , we observe that there exist two framed double tori L and G in M that intersect S transveresly, and such that L \ S consists of two disjoint longitudes of S and G \ S consists of two disjoint meridians. Following the construction of P we see that L and G are lifted in P to framed closed surfaces and , respectively, that intersect transversely, and such that \ consists of two disjoint longitudes of and \ consists of two disjoint meridians. By construction of the volume element and the vector eld on P , if the element [f ] 2 H 1 (P ;Z) corresponds via the above splitting to the homotopy class of the projection onto the longitude on , then
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