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本文研究A(m)-代数的形变理论,利用A(m)-代数上同调定义了形变后的障碍,获得了形变与障碍的关系,为A(m)-代数的形变结构提供了研究理论基础. 相似文献
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We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O(k-VERTEX COVER) and call it the set of obstructions. Our main result is to give a tight vertex bound of O(k-VERTEX COVER), and then confirm a conjecture made by Liu Xiong that there is a unique connected obstruction with maximum number of vertices for k-VERTEX COVER and this graph is C2k+1. We also find two iterative methods to generate graphs in O((k+1)-VERTEX COVER) from any graph in O(k-VERTEX COVER). 相似文献
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We discuss new obstructions to positive sectional curvature and symmetry. The main result asserts that the index of the Dirac operator twisted with the tangent bundle vanishes on a 2-connected manifold of dimension ≠8 if the manifold admits a metric of positive sectional curvature and isometric effective S1-action. The proof relies on the rigidity theorem for elliptic genera and properties of totally geodesic submanifolds. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(3):605-626
In this paper we study the bilinear-control problem for the linear and non-linear Schrödinger equation with harmonic potential. By the means of different examples, we show how space-time smoothing effects (Strichartz estimates, Kato smoothing effect) enjoyed by the linear flow, can help to prove obstructions to controllability. 相似文献
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In Hanke and Schick (J Differ Geom 74(2):293–320, 2006) we showed non-vanishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from
Gromov and Lawson (Ann Math 111(2):209–230, 1980), involving contracting maps defined on finite covers of the given manifolds.
In the paper at hand, we weaken this assumption to the one in Gromov and Lawson (Publ IHES 58:83–196, 1983) where infinite
covers are allowed. The new idea is the construction of a geometrically given C*-algebra with trace which encodes the information given by these infinite covers. Along the way we obtain an easy proof of
a relative index theorem relevant in this context.
We thank S. Stolz and A. Thom for useful conversations regarding the research in this paper. Both authors are members of the
DFG emphasis programme “Globale Differentialgeometrie” whose support is gratefully acknowledged. 相似文献
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