Analytic Topology of Groups, Actions, Strings and Varietes
英文摘要:
This is a paper in Analytic Topology.
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Alexander Reznikov
This is a paper in Analytic Topology.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new observations. We further discuss how nonnilpotent local level homology classes with respect to the Chas-Sullivan and the Goresky-Hingston product detect closed geodesics with optimal index growth rates.
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.
String topology operations under Chen's iterated integrals and homotopy transfer
为关联链级\(S^1\)等变弦拓扑与微扰陈 - 西蒙斯理论的构形空间积分建立分析基础,证明陈的迭代积分与同伦转移的复合交织同调上的对合李双代数结构。
On the string topology of symmetric spaces of higher rank
该研究探讨了高阶对称空间的字符串拓扑性质,揭示了Chas-Sullivan乘积的非平凡性及基于循环空间的余乘积的平凡性。
On the invariance of the string topology coproduct
研究弦拓扑余积在同伦等价下不变性失效问题,给出基于同伦数据及“伪对角线”构建阻碍类的奈夫公式变体,此阻碍类可衡量同伦等价有界性,且决定余积到高维环路推广的不变性失效。
We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent a…
Topology of low-dimensional generalized Ricci solitons and string backgrounds
该研究证明低维广义Ricci孤立子的微分同胚类型,确定三类弦背景的拓扑约束,明确多数弦背景无法与对应经典特殊全纯性流形共存,并刻画BHE三维流形的拓扑。
We present an explicit formula for the topology and H-flux of the T-dual of a general type II compactification, significantly generalizing earlier results. Our results apply to T-dualities with respect to any circle action on spacetime. As before, T-duality exchanges type IIA and type IIB string theories. A new consequence is that the T-dual spacetime is a singular space when the fixed point set is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges of type II string theories on the singular dual are classified by twisted equivariant coh…
Let M be a closed Riemannian manifold. We extend the product of Goresky-Hingston, on the cohomology of the free loop space of M relative to the constant loops, to a nonrelative product. It is graded associative and commutative, and compatible with the length filtration on the loop space, like the original product. We prove the following new geometric property of the dual homology coproduct: the nonvanishing of the k-th iterate of the coproduct on a homology class ensures the existence of a loop with a (k+1)-fold self-intersection in every representative of the class. For spheres and projective…
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