ON INTERSECTION AND TRANSVERSALITY OF MAPS
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Amer Mathematical Soc
American Mathematical Society (AMS)
American Mathematical Society (AMS)
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Given a smooth map fV: V-+ K with f*V(nu K) = nu V, a gen-eral question arises: under which conditions there exists a smooth extension f : M-+ N of fV such that f is transverse to K and f-1(K) = V, where M, N are smooth closed manifolds of dimension m and n, V, K are closed submanifolds of M and N, respectively, of same codimension and nu K, nu V are the normal bundles of K in N and V in M, respectively. In this paper, we give conditions to the existence of extensions, by using bordism intersection pro d-uct. Moreover, we present an interesting and non-trivial example illustrating the systematic construction of such extensions, skeletonwise.
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Proceedings of the American Mathematical Society. Providence: Amer Mathematical Soc, 12 p., 2023.
