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作者：Buczolich, Zoltan; Mauldin, R. Daniel
摘要：In this paper we answer a question of J. Bourgain which was motivated by questions A. Bellow and H. Furstenberg. We show that the sequence {n(2)}(n=1)(infinity) L-1-universally bad. This implies that it is not true that given a dynamical system. (X, Sigma, mu, T) and f is an element of L-1(mu), the ergodic means lim(N ->infinity) 1/N Sigma(N)(n=1) f(T-n2(x)) converge almost surely.
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作者：van Erp, Erik
摘要：We present a new solution to the index problem for hypoelliptic operators in the Heisenberg calculus on contact manifolds, by constructing the appropriate topological K-theory cocycle for such operators. Its Chern character gives a cohomology class to which the Atiyah-Singer index formula can be applied. Such a K- cocycle has already been constructed by Boutet de Monvel for Toeplitz operators, and, more recently, by Melrose and Epstein for the class of Hermite operators. Our construction appli...
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作者：Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
摘要：We show that almost nonnegatively curved m-manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.
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作者：Neeman, Amnon
摘要：Let R be a ring. In a previous paper [11] we found a new description for the category K(R-Proj); it is equivalent to the Verdier quotient K(R-Flat)/S, for some suitable S subset of K(R-Flat). In this article we show that the quotient map from K(R-Flat) to K(R-Flat)/S always has a right adjoint. This gives a new, fully faithful embedding of K(R-Proj)ninto K(R-Flat). Its virtue is that it generalizes to nonaffine schemes.
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作者：Sarkar, Sucharit; Wang, Jiajun
摘要：In this paper, we give an algorithm to compute the hat version of Heegaard Floer homology of a closed oriented three-manifold. This method also allows us to compute the filtration coming from a null-homologous link in a three-manifold.
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作者：Arezzo, Claudio; Pacard, Frank
摘要：In this paper we prove the existence of Kahler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold that already carries a constant scalar curvature Kahler metric. In the case where the manifold has nontrivial holomorphic vector fields with zeros, we give necessary conditions on the number and locations of the blow up points for the blow up to carry constant scalar curvature Kahler metrics.
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作者：Jorgenson, Jay; Kramer, Juerg
摘要：Let X be a compact Riemann surface of genus g(X) >= 1. In 1984, G. Faltings introduced a new invariant delta(Fal) (X) associated to X. In this paper we give explicit bounds for delta(Fal)(X) in terms of fundamental differential geometric invariants arising from X, when g(X) > 1. As an application, we are able to give bounds for Faltings's delta function for the family of modular curves X-0(N) in terms of the genus only. In combination with work of A. Abbes, P. Michel and E. Ullmo, this leads t...
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作者：Debacker, Stephen; Reeder, Mark
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作者：Freedman, Michael H.
摘要：Complexity theory, being the metrical version of decision theory, has long been suspected of harboring undecidable statements among its most prominent conjectures. Taking this possibility seriously, we add one such conjecture, P-#P not equal NP, as a new axiom and find that it has an implication in 3-dimensional topology. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.
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作者：Farrell, F. Thomas; Ontaneda, Pedro
摘要：For a smooth manifold M we define the Teichmuller space I(M) of all Riemannian metrics on M and the Teichmuller space I-is an element of(M) of epsilon-pinched negatively curved metrics on M, where 0 <= is an element of <= infinity. We prove that if M is hyperbolic, the natural inclusion I-is an element of(M) curved right arrow I(M) is, in general, not homotopically trivial. In particular, I-is an element of(M) is, in general, not contractible.
