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η-INVARIANT AND CHERN-SIMONS CURRENT 被引量:2
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作者 ZHANGWEIPING 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第1期45-56,共12页
The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localizati... The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator. 展开更多
关键词 Direct image η-invariant Chern-Simons current mod k index theorem
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SUB-SIGNATURE OPERATORS,η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES 被引量:1
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作者 ZHANGWEIPING 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第1期7-36,共30页
The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In part... The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2,3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants. 展开更多
关键词 Sub-signature operators η-invariants Flat vector bundles Riemann-Roch
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On the μ-invariant of two-variable primitive p-adic L-functions 被引量:1
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作者 KANG YunLing QIN HouRong 《Science China Mathematics》 SCIE 2014年第6期1149-1154,共6页
Using the idea of Sinnott,Gillard and Schneps,we prove theμ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang(2012),which arises naturally in the study of Iwasawa theory for an el... Using the idea of Sinnott,Gillard and Schneps,we prove theμ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang(2012),which arises naturally in the study of Iwasawa theory for an elliptic curve with complex multiplication(CM). 展开更多
关键词 CM elliptic curve p-adic L-function μ-invariant
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On U(n)-invariant strongly convex complex Finsler metrics 被引量:1
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作者 Kun Wang Hongchuan Xia Chunping Zhong 《Science China Mathematics》 SCIE CSCD 2021年第11期2461-2478,共18页
In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between... In this paper,we obtain a necessary and sufficient condition for a U(n)-invariant complex Finsler metric F on domains in C^(n) to be strongly convex,which also makes it possible to investigate the relationship between real and complex Finsler geometries via concrete and computable examples.We prove a rigid theorem which states that a U(n)-invariant strongly convex complex Finsler metric F is a real Berwald metric if and only if F comes from a U(n)-invariant Hermitian metric.We give a characterization of U(n)-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of the U(n)-invariant strongly pseudoconvex complex Finsler metric.Finally,we prove that the real geodesics of some U(n)-invariant complex Finsler metric restricted on the unit sphere S^(2n-1)■C^(n) share a specific property as that of the complex Wrona metric on C^(n). 展开更多
关键词 U(n)-invariant complex Finsler metric strongly convex real Berwald metric holomorphic curvature
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η-Invariant and Flat Vector Bundles
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作者 Xiaonan MA Weiping ZHANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第1期67-72,共6页
We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to(not necessary unitary )flat vector bundles,which identifies explicitly its realandimaginary parts.This... We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to(not necessary unitary )flat vector bundles,which identifies explicitly its realandimaginary parts.This is done by combining a deformation of flatconnections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah Patodi and Singer. 展开更多
关键词 Flat vector bundle η-invariant ρ-invariant
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GL(n, R)-Equivalence of a Pair of Curves in Terms of Invariants
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作者 Yasemin Sagiroglu Ziya Yapar 《Journal of Mathematics and System Science》 2016年第1期16-22,共7页
In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl(n,R). The conditions of G = Gl(n, R) -equivalence of a pair of curves are found in terms of G = Gl(n, R)-invariants... In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl(n,R). The conditions of G = Gl(n, R) -equivalence of a pair of curves are found in terms of G = Gl(n, R)-invariants. And the independence of GL(n, R) -invariants is shown. 展开更多
关键词 GL(n R) -invariants differential invariants of curves equivalence of curves.
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WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C-ALGEBRA ?
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作者 WU LIANGSEN (Institute of Mathematics, East Normal University, Shanghai 200062. China) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1994年第2期153-156,共4页
Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant s... Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞). 展开更多
关键词 C-ALGEBRA Stable algebra Cuntz algebra α-invariance.
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