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91.
Howard Jacobowitz 《Transactions of the American Mathematical Society》2006,358(10):4521-4531
This paper studies a generic class of sub-bundles of the complexified tangent bundle. Involutive, generic structures always exist and have Levi forms with only simple zeroes. For a compact, orientable three-manifold the Chern class of the sub-bundle is mod equivalent to the Poincaré dual of the characteristic set of the associated system of linear partial differential equations.
92.
Y.X.zhao 《Frontiers of Physics》2020,15(1):13603-69,F0004
It was understood that Chern insulators cannot be realized in the presence of PT symmetry.In this paper,we reveal a new class of PT-symmetric Chern insulators,which has internal degrees of freedom forming real representations of a symmetry group with a complex endomorphism field.As a generalization to the conventional 2n-dimensional Chern insulators with integer n≥1,these PT-symmetric Chern insulators have the n-th complex Chern number as their topological invariant,and have a Z classification given by the equivariant orthogonal K theory.Thus,in a fairly different sense,there exist ubiquitously Chern insulators with PT.symmetry.By generalizing the Thouless charge pump argument,we find that,for a PT-symmetric Chern insulator with Chern number v.there are equally many v flavors of coexisting left-and right-handed chiral modes.Chiral modes with opposite chirality are complex conjugates to each other as complex representations of the internal symmetry group,but are not isomorphic.For the physical dimensionality d=2,the PT-symmetric Chern insulators may be realized in artificial systems including photonic crystals and periodic mechanical systems. 相似文献
93.
Donu Arapura 《代数通讯》2013,41(4):1153-1167
Constraints on the Chern classes of a vector bundle on a possibly singular algebraic variety are found, which are stronger than the obvious Hodge theoretic constraints. This is done by showing that these lift to Chern classes in the hypercohomology of the complex of Kähler differentials. 相似文献
94.
Wei WANG 《数学年刊B辑(英文版)》2017,38(6):1353-1364
This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus.By using the equivariant Riemann-Roch relation of AtiyahHirzebruch type,it is proved that the vanishing of equivariant cohomology Chern numbers is equivalent to the vanishing of equivariant K-theoretic Chern numbers. 相似文献
95.
This paper is concerned with Chern‐Ricci flow evolution of left‐invariant hermitian structures on Lie groups. We study the behavior of a solution, as t is approaching the first time singularity, by rescaling in order to prevent collapsing and obtain convergence in the pointed (or Cheeger‐Gromov) sense to a Chern‐Ricci soliton. We give some results on the Chern‐Ricci form and the Lie group structure of the pointed limit in terms of the starting hermitian metric and, as an application, we obtain a complete picture for the class of solvable Lie groups having a codimension one normal abelian subgroup. We have also found a Chern‐Ricci soliton hermitian metric on most of the complex surfaces which are solvmanifolds, including an unexpected shrinking soliton example. 相似文献
96.
97.
Let V be a compact complex analytic subset of a non-singular holomorphic manifold M. Assume that V has pure complex dimension n. Denote by V0 its regular part, and by [V] its fundamental class in H2n(V;
). If V is a locally complete intersection (LCI), it is known that the normal bundle NV_0 in M to V0 in M has a natural extension NV to all of V, so that we can define its Chern classes c(*)(NV) in cohomology, as well as the Chern classes cvir(*). If V is a locally complete intersection (LCI), it is known that the normal bundle NV_0 in M to V0 in M has a natural extension NV to all of V, so that we can define its Chern classes c(*)(NV) in cohomology, as well as the Chern classes cvir(*)
(V) of the virtual tangent bundle Tvir(V):=[TM|V - NV] in the K-theory K0(V). This has applications
In the general case, we can no more define NV and Tvir(V). However we shall associate, to each desingularisation of V, Chern classes cn-*(NV, ) and
in the homology H2(n-*)(V), which coincide respectively with the Poincaré duals
and
of the cohomological Chern classes c(*)(NV) and c
vir(*)(V) when V is LCI. Our classes do not coincide with the inverse Segre classes and the Fulton–Johnson classes respectively, except for LCIs. Moreover, it turns out that this is sufficient for being able to generalize to compact pure dimensional complex analytic subsets of a holomorphic manifold the two kinds of applications mentioned above. These constructions depend on in general. However, in the case of curves, there is only one desingularisation, so that all these constructions become intrinsic.Mathematics Subject Classification: 57R20, 57R25, 19E20. 相似文献
| on one hand to the definition of various indices associated to a singular foliation on M with respect to which V is invariant (cf. [23–25]), and |
| on the other hand to the definition of the Milnor numbers and classes of the singular part of V (cf. [7,8]). |
98.
The well-known Yau's uniformization conjecture states that any complete noncompact K¨ahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed by G. Liu in [23]. In the first part, we will give a survey on the progress.In the second part, we will consider Yau's conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number C_1~n is an essential condition to solve Yau's conjecture by using algebraic embedding method. Moreover, we prove that,under bounded curvature conditions, C_1~n is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau's uniformization conjecture on K¨ahler manifolds with minimal volume growth. 相似文献
99.
从Faddeev Popov(FP)方法对规范理论给出的位形空间生成泛函出发,导出了位形空间非定域变换下的Ward恒等式。应用于非Abel Chern Simons(CS)理论,得到了CS规范场鬼场正规顶角间的Ward恒等,并把此结果与文献[1]做了对比,对规范理论用位形空间路径积分讨论更简便。 相似文献
100.
Sandra Di Rocco Andrew J. Sommese 《Transactions of the American Mathematical Society》2004,356(2):587-598
This article shows a number of strong inequalities that hold for the Chern numbers , of any ample vector bundle of rank on a smooth toric projective surface, , whose topological Euler characteristic is . One general lower bound for proven in this article has leading term . Using Bogomolov instability, strong lower bounds for are also given. Using the new inequalities, the exceptions to the lower bounds 4e(S)$"> and e(S)$"> are classified.