An average intersection estimate for families of diffeomorphisms
Abstract
We show that for any sufficiently rich compact family H of C1 diffeomorphisms of a closed Riemannanian manifold M, the average geometric intersection number over h ∈ H between h(V) and W, for V, W any complementary dimensional submanifolds of M, is approximately (i.e. up to a uniform multiplicative error depending only on H) the product of their volumes. We also give a construction showing that such families always exist.
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