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作者：Shiota, Masahiro
作者单位：Nagoya University
摘要：Milnor discovered two compact polyhedra which are homeomorphic but not PL homeomorphic (a counterexample to the Hauptvermutung). He constructed the homeomorphism by a finite procedure repeated infinitely often. Informally, we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times. In this sense, Milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra. In the case where the homeomorphism is semia...
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作者：Hertz, Federico Rodriguez; Wang, Zhiren
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Yale University
摘要：We show that all Anosov -actions on tori and nilmanifolds without rank-one factor actions are, up to conjugacy, actions by automorphisms.
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作者：Hersh, Patricia
作者单位：North Carolina State University
摘要：Fomin and Shapiro conjectured that the link of the identity in the Bruhat stratification of the totally nonnegative real part of the unipotent radical of a Borel subgroup in a semisimple, simply connected algebraic group defined and split over is a regular CW complex homeomorphic to a ball. The main result of this paper is a proof of this conjecture. This completes the solution of the question of Bernstein of identifying regular CW complexes arising naturally from representation theory having ...
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作者：Mayboroda, Svitlana; Maz'ya, Vladimir
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Liverpool; Linkoping University
摘要：The present paper establishes boundedness of derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of , 2a parts per thousand currency signna parts per thousand currency sign2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.
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作者：Parimala, R.; Suresh, V.
作者单位：Emory University
摘要：Let K be a complete discretely valued field with residue field kappa and F the function field of a curve over K. Let p be the characteristic of kappa and a a prime not equal to p. If the Brauer a-dimensions of all finite extensions of kappa are bounded by d and the Brauer a-dimensions of all extensions of kappa of transcendence degree at most 1 are bounded by d+1, then it is known that the Brauer a-dimension of F is at most d+2 (Lieblich in J. Reine Angew. Math. 659:1-41, 2011; Saltman in J. R...
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作者：Petersen, Dan; Tommasi, Orsola
作者单位：Royal Institute of Technology; Leibniz University Hannover
摘要：We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring is not Gorenstein. In fact, our N equals the smallest integer such that there is a non-tautological cohomology class of even degree on . By work of Graber and Pandharipande, such a class exists on , and we present some evidence indicating that N is in fact 20.
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作者：Grabowski, Lukasz
作者单位：University of Warwick
摘要：Main theorems of the article concern the problem of Atiyah on possible values of -Betti numbers. It is shown that all non-negative real numbers are -Betti numbers, and that many (for example all non-negative algebraic) real numbers are -Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental -Betti number with respect to an action of the threefold direct product...
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作者：Geiges, Hansjoerg; Roettgen, Nena; Zehmisch, Kai
作者单位：University of Cologne; University of Freiburg
摘要：We construct a contact form on , , equal to the standard contact form outside a compact set and defining the standard contact structure on all of , which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.
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作者：Gupta, Neena
作者单位：Tata Institute of Fundamental Research (TIFR)
摘要：We show that the Cancellation Conjecture does not hold for the affine space A(k)(3) over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X (1), X (2), X (3)] although A[T] is isomorphic to k[X (1), X (2), X (3), X (4)].
