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作者：Ekholm, Tobias; Ng, Lenhard; Shende, Vivek
作者单位：Uppsala University; Royal Swedish Academy of Sciences; Mittag-Leffler Institute; Duke University; University of California System; University of California Berkeley
摘要：We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtai...
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作者：Gompf, Robert E.
作者单位：University of Texas System; University of Texas Austin
摘要：We provide the first information on diffeotopy groups of exotic smoothings of R-4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group actions. There are also actions at infinity by non-finitely generated groups, for which no nontrivial element extends over the whole manifold. In contrast, every diffeomorphism of the end of the universal R4 extends. Our techniques apply to many other open 4-mani...
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作者：Groechenig, Karlheinz; Romero, Jose Luis; Stoeckler, Joachim
作者单位：University of Vienna; Dortmund University of Technology; Austrian Academy of Sciences
摘要：We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as for (in which case g is called totally positive of Gaussian type). In analogy to Beurling's sampling theorem for the Paley-Wiener space of entire functions, we prove that every separated set with lower Beurling density is a sampling set for the shift-invariant space generated by such a g. In view of the known nece...
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作者：Tsukamoto, Masaki
作者单位：Kyoto University
摘要：Mean dimension is a topological invariant of dynamical systems counting the number of parameters averaged by dynamics. Brody curves are Lipschitz holomorphic maps , and they form an infinite dimensional dynamical system. Gromov started the problem of estimating its mean dimension in 1999. We solve this problem by proving the exact mean dimension formula. Our formula expresses the mean dimension by the energy density of Brody curves. As a key novel ingredient, we use an information theoretic ap...
