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1.
Let M be a hypersurface in a simply connected space form . We prove some rigidity results for M in terms of lower bounds on the Ricci curvature of the hypersurface M.  相似文献   

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Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the uniqueness) of an LU-invariant probability measure on a distributional completion of the loop space of X.  相似文献   

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We deduce a system of ODEs describing the behavior of critical points and poles of a smooth one-parametric family of rational functions uniformizing a given family of ramified coverings of the Riemann sphere.  相似文献   

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The purpose of this paper is to calculate the rational cohomology ${H^{\ast}(X^{{S}^{1}} ; \mathbb{Q})}$ of the free loop space for a simply connected closed 4-manifold X. We use minimal models, so the starting point is the cohomology algebra ${H^{\ast}(X; \mathbb{Q})}$ which depends only on the second Betti number b 2 and the signature of X itself. Calculations of ${H^{\ast}(X^{{S}^{1}} ; \mathbb{Q})}$ for b 2 ≤ 2 are known. We study the case b 2 > 2. We obtain an explicit formula for Poincaré series of the space ${X^{{S}^{1}}}$ , with the second Betti number b 2 as a parameter.  相似文献   

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We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form. Work partially supported by a DGICYT Grant No. PB91-0324 and by the E.C. Contract CHRX-CT92-0050 “G.A.D.G.E.T. II”  相似文献   

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Let A be a representation-finite simply connected algebra, and TAbe an arbitrary tilting module (in the sense of Happei and Ringel). We show that B = End TA satisfies the separation condition of Bautista, Larrion and Salmeron. This implies that B is also simply connected.  相似文献   

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It is well-known that simply connected algebras are uniquely determined by a graded tree.Reversely,each graded tree gives rise to a not necessarily representation-finite algebra. We call an algebra critical provided it is not representation-finite, but any proper convex full subalgebra is.All critical algebras arising from graded trees are classified.  相似文献   

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The iterative method of Wegmann (1978) for conformal mapping of a region E to a region G is reformulated in terms of a conjugation operator. If the boundary of G is sufficiently smooth, the method converges quadratically in a Sobolev space W. To overcome the crowding an elongated canonical region E should be chosen if the image region G is elongated. For ellipses E the operator of conjugation can be expressed in a very simple way in terms of Fourier series. Numerically, this can be performed very efficiently by fast Fourier transform (FFT).  相似文献   

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The purpose of this paper is: (i) to construct a space which is semilocally simply connected in the sense of Spanier even though its Spanier group is non-trivial; (ii) to propose a modification of the notion of a Spanier group so that via the modified Spanier group semilocal simple connectivity can be characterized; and (iii) to point out that with just a slightly modified definition of semilocal simple connectivity which is sometimes also used in literature, the classical Spanier group gives the correct characterization within the general class of path-connected topological spaces.While the condition “semilocally simply connected” plays a crucial role in classical covering theory, in generalized covering theory one needs to consider the condition “homotopically Hausdorff” instead. The paper also discusses which implications hold between all of the abovementioned conditions and, via the modified Spanier groups, it also unveils the weakest so far known algebraic characterization for the existence of generalized covering spaces as introduced by Fischer and Zastrow. For most of the implications, the paper also proves the non-reversibility by providing the corresponding examples. Some of them rely on spaces that are newly constructed in this paper.  相似文献   

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This work was supported by NSF Grant DMS 92-04092 and an Alfred P. Sloan Research Fellowship.  相似文献   

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If G is a group and an automorphism of G, one has the twisted conjugation action of G on itself This paper collects a number of results — more or less well known — for the case that G is a simply connected semisimple group.  相似文献   

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h-cobordisms between simply connected 4-manifolds are studied. It is shown that most inertial h-cobordisms have a handle decomposition with one 2-handle and one 3-handle, and h-cobordisms between nondiffeomorphic manifolds have handle decompositions with the minimal number of handles consistent with a diffeomorphism between the stabilized ends. Also the number of distinct h-cobordisms between two fixed manifolds is described in terms of isomorphisms of their quadratic forms. These results are applied to Dolgachev surfaces and the Kummer surface using recent work of Donaldson, Friedman and Morgan, and Matumoto.  相似文献   

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In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two bars is NP-complete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solved in quadratic time (in the area). We prove that there is a finite set of at most 106 rectangles for which the tileability problem of simply connected regions is NP-complete, closing the gap between positive and negative results in the field. We also prove that counting such rectangular tilings is #P-complete, a first result of this kind.  相似文献   

17.
We prove that the ratio of the minimum number of rectangles covering a simply connected board (polyomino)B and the maximum number of points inB no two of which are contained in a common rectangle is less than 2. This research was partially supported by MEV (Budapest).  相似文献   

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Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset.  相似文献   

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