共查询到20条相似文献,搜索用时 15 毫秒
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A canonically defined mod 2 linear dependency current is associated to each collection v of sections, v1,…,vm, of a real rank n vector bundle. This current is supported on the linear dependency set of v. It is defined whenever the
collection v satisfies a weak measure theoretic condition called “atomicity.” Essentially any reasonable collection of sections
satisfies this condition, vastly extending the usual general position hypothesis. This current is a mod 2 d-closed locally
integrally flat current of degree q = n −m + 1 and hence determines a ℤ2-cohomology class. This class is shown to be well defined independent of the collection of sections. Moreover, it is the qth
Stiefel-Whitney class of the vector bundle.
More is true if q is odd or q = n. In this case a linear dependency current which is twisted by the orientation of the bundle
can be associated to the collection v. The mod 2 reduction of this current is the mod 2 linear dependency current. The cohomology
class of the linear dependency current is 2-torsion and is the qth twisted integral Stiefel-Whitney class of the bundle.
In addition, higher dependency and general degeneracy currents of bundle maps are studied, together with applications to singularities
of projections and maps.
These results rely on a theorem of Federer which states that the complex of integrally flat currents mod p computes cohomology
mod p. An alternate approach to Federer’s theorem is offered in an appendix. This approach is simpler and is via sheaf theory. 相似文献
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In this note we parameterize the Stiefel manifold Stk,n in a manner that allows to perform a constrained Newton step in a relatively simple way. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Charles P. Boyer Krzysztof Galicki Benjamin M. Mann 《Annals of Global Analysis and Geometry》1996,14(1):81-105
This paper describes a family of hypercomplex structures {% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFqessaaa!4076!\[\mathcal{I}\]a(p)}a=1,2,3 depending on n real non-zero parameters p = (p
1,...,p
n) on the Stiefel manifold of complex 2-planes in n for all n > 2. Generally, these hypercomplex structures are inhomogenous with the exception of the case when all the p
i's are equal. We also determine the Lie algebra of infinitesimal hypercomplex automorphisms for each structure. Furthermore, we solve the equivalence problem for the hypercomplex structures in the case that the components of p are pairwise commensurable. Finally, some of these examples admit discrete hypercomplex quotients whose topology we also analyze.During the preparation of this work all three authors were supported by NSF grants. 相似文献
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《European Journal of Operational Research》2002,143(2):365-376
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The complex Stiefel manifolds admit a stable decomposition asThom spaces of certain bundles over Grassmannians. The purposeof the paper is to identify the splitting in any complex orientedcohomology theory. 相似文献
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Daisuke Kishimoto 《Topology and its Applications》2007,154(7):1465-1469
By calculating certain generalized cohomology theory, lower bounds for the L-S category of quaternionic Stiefel manifolds are given. 相似文献
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We characterize the optimal solution of a quadratic program over the Stiefel manifold with an objective function in trace formulation. The result is applied to relaxations of HQAP and MTLS. Finally, we show that strong duality holds for the Lagrangian dual, provided some redundant constraints are added to the primal program. 相似文献
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The Riemann space whose elements are m × k (m k) matrices X, i.e., orientations, such that X′X = Ik is called the Stiefel manifold Vk,m. The matrix Langevin (or von Mises-Fisher) and matrix Bingham distributions have been suggested as distributions on Vk,m. In this paper, we present some distributional results on Vk,m. Two kinds of decomposition are given of the differential form for the invariant measure on Vk,m, and they are utilized to derive distributions on the component Stiefel manifolds and subspaces of Vk,m for the above-mentioned two distributions. The singular value decomposition of the sum of a random sample from the matrix Langevin distribution gives the maximum likelihood estimators of the population orientations and modal orientation. We derive sampling distributions of matrix statistics including these sample estimators. Furthermore, representations in terms of the Hankel transform and multi-sample distribution theory are briefly discussed. 相似文献
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Nelza E. Barufatti Derek Hacon 《Transactions of the American Mathematical Society》2000,352(7):3189-3209
Using the Hodgkin spectral sequence we calculate , the complex -theory of the projective Stiefel manifold , for even. For odd, we are only able to calculate , but this is sufficient to determine the order of the complexified Hopf bundle over .
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L. Astey S. Gitler E. Micha G. Pastor 《Proceedings of the American Mathematical Society》2000,128(5):1527-1530
The question of parallelizability of the complex projective Stiefel manifolds is settled.
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基于Stiefel流形上算法的几何框架,本文提出了Stiefel流形上的梯度下降法.理论上给出了算法收敛性定理.三个数值仿真算例表明算法是有效的,与其他方法相比具有更快的收敛速度. 相似文献