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作者：Birman, Joan S.; Hilden, Hugh M.
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作者：Klingler, Bruno
摘要：An affine manifold X in the sense of differential geometry is a differentiable manifold admitting an atlas of charts with value in an affine space, with locally constant affine change of coordinates. Equivalently, it is a manifold whose tangent bundle admits a flat torsion free connection. Around 1955 Chern conjectured that the Euler characteristic of any compact affine manifold has to vanish. In this paper we prove Chern's conjecture in the case where X moreover admits a parallel volume form.
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作者：Foscolo, Lorenzo; Haskins, Mark
摘要：There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G(2) : the metric cone over a Riemannian 6-manifold M has holonomy contained in G(2) if and only ...
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作者：Calabri, A.; Ciliberto, C.; Flamini, F.; Miranda, R.
摘要：We correct an error in the Multiple Point Formula (7.3) in the paper mentioned in the title. This correction propagates to formulas (7.5), (7.6), (7.23) and (8.18), and it affects minor results in Section 8, where few statements require an extra assumption, but it does not affect the main results of Section 8.
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作者：Temkin, Michael
摘要：We strengthen Gabber's l'-alteration theorem by avoiding all primes invertible on a scheme. In particular, we prove that any scheme X of finite type over a quasi-excellent threefold can be desingularized by a char(X)alteration, i.e., an alteration whose order is only divisible by primes noninvertible on X. The main new ingredient in the proof is a tame distillation theorem asserting that, after enlarging, any alteration of X can be split into a composition of a tame Galois alteration and a cha...
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作者：Blumenthal, Alex; Xue, Jinxin; Young, Lai-Sang
摘要：We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the standard map. Lower bounds for Lyapunov exponents of such systems are very hard to estimate, due to the potential switching of stable and unstable directions. This paper shows that with the addition of (very) small random perturbations, one obtains with relative ease Lyapunov exponents reflectin...
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作者：Ettinger, Boris; Lindblad, Hans
摘要：We are concerned with how regular initial data have to be to ensure local existence for Einstein's equations in wave coordinates. Klainerman-Rodnianski and Smith-Tataru showed that there in general is local existence for data in Sobolev spaces H<^>s with regularity s>2. We give an example of data in Sobolev spaces with regularity s=2 for which there is no local solution in this space.
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作者：Cadoret, Anna; Hui, Chun-Yin; Tamagawa, Akio
摘要：Let X be a connected scheme, smooth and separated over an algebraically closed field k of characteristic p >= 0, let f : Y -> X be a smooth proper morphism and x a geometric point on X. We prove that the tensor invariants of bounded length <= d of pi(1)(X, x) acting on the etale cohomology groups H* (Y-x, F-l) are the reduction modulo-l of those of pi(1)(X, x) acting on H* (Y-x, Z(l)) for l greater than a constant depending only on f : Y -> X, d. We apply this result to show that the geometric...
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作者：Galatius, Soren; Randal-Williams, Oscar D.
摘要：We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n, for attaching handles of index at least n, after these manifolds have been stabilised by countably many copies of S-n x S-n. Combined with previous work of the authors, we obtain an analogue of the Madsen Weiss theorem for any simply -connected manifold of dimension 2n >= 6.
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作者：Croot, Ernie; Lev, Vsevolod F.; Pach, Peter Pal
