Singular Foliations: Desingularization and the Baum-Connes Conjecture

奇异叶状结构:去奇异化和鲍姆-康尼斯猜想

基本信息

  • 批准号:
    272988935
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    德国
  • 项目类别:
    Research Grants
  • 财政年份:
    2015
  • 资助国家:
    德国
  • 起止时间:
    2014-12-31 至 2015-12-31
  • 项目状态:
    已结题

项目摘要

Singular foliations are examples of dynamical systems and they appear in an abundance of geometric situations, such as actions of Lie groups and Poisson geometry. In fact, Poisson structures are completely determined by their associated singular foliation (symplectic). To work with singular foliations and to understand them requires precisely because of their singular nature the development of new tools. The dynamics of a (singular foliation) is encoded in its holonomy groupoid and the associated groupoid C*-algebra. To understand those, one must understand their K-theory, most commonly via a Baum-Connes conjecture.The first big open question to do this is the construction of the expectedanswer: the classifying space for proper action of thesingular foliation. We propose to achieve this using higher order (higher Liecategory) methods. This will be done as a completedesingularization of singular foliation (via suitable resolutions). Namely, the problem is to find a space withenough differentiable structure, which acts as a model for the leaf space.A final goal then is the application of these methods for the calculation ofthe spectrum of Schrödinger type operators along the singular foliation.
奇异叶理是动力系统的例子,它们出现在丰富的几何情况下,如李群和泊松几何的作用。事实上,泊松结构完全由其相关的奇异叶理(辛)决定。研究奇异的叶理并理解它们,正是因为它们的奇异性质,需要开发新的工具。一个(奇异叶理)的动力学被编码在它的完整群胚和相关的群胚C*-代数中。为了理解这些,人们必须理解他们的K理论,最常见的是通过鲍姆-康纳斯猜想。要做到这一点,第一个大的开放问题是预期答案的构建:奇异叶理的正确作用的分类空间。 我们建议使用高阶(高阶)方法来实现这一点。这将作为奇异叶理的完全去奇异化(通过适当的分辨率)来完成。即寻找一个具有足够可微结构的空间作为叶空间的模型,最终目标是将这些方法应用于计算薛定谔型算子沿着奇异叶理的谱.

项目成果

期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves
StefanâSussmann 奇异叶状结构、奇异子代数体及其相关滑轮
Almost regular Poisson manifolds and their holonomy groupoids
几乎正则泊松流形及其完整群群
  • DOI:
    10.1007/s00029-017-0319-5
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    I. Androulidakis;M. Zambon
  • 通讯作者:
    M. Zambon
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Professor Dr. Thomas Schick其他文献

Professor Dr. Thomas Schick的其他文献

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{{ truncateString('Professor Dr. Thomas Schick', 18)}}的其他基金

Large scale index, positive scalar curvature and manifold topology
大尺度指数、正标量曲率和流形拓扑
  • 批准号:
    321324296
  • 财政年份:
    2016
  • 资助金额:
    --
  • 项目类别:
    Research Grants
L2-invariants of groups
群的 L2 不变量
  • 批准号:
    144856302
  • 财政年份:
    2009
  • 资助金额:
    --
  • 项目类别:
    Research Grants
L2-invariants
L2 不变量
  • 批准号:
    42819878
  • 财政年份:
    2007
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes
Coarse geometry and applications to the Baum-Connes conjecture
粗略几何及其在 Baum-Connes 猜想中的应用
  • 批准号:
    23527961
  • 财政年份:
    2006
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Index theoretic approaches to the classification of positive scalar curvature
正标量曲率分类的索引理论方法
  • 批准号:
    5406956
  • 财政年份:
    2003
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes
Geometric Chern characters for p-adic equivariant K-theory and K-homology
p 进等变 K 理论和 K 同调的几何 Chern 特征
  • 批准号:
    441787895
  • 财政年份:
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes

相似海外基金

Conference: St. Louis Topology Conference: Flows and Foliations in 3-Manifolds
会议:圣路易斯拓扑会议:3 流形中的流动和叶理
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    2350309
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    2024
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Minimal Models of Foliations
叶状结构的最小模型
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    EP/X029387/1
  • 财政年份:
    2023
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    --
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    Research Grant
Integral Subvarieties for Foliations on Shimura Varieties in Positive Characterstic.
志村品种正面性状叶的完整亚品种。
  • 批准号:
    546746-2020
  • 财政年份:
    2022
  • 资助金额:
    --
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Impact des défoliations de la tordeuse des bourgeons de l'épinette (TBE) et des arrosages de Bacillus thuringiensis ssp kurstaki (Btk) sur l'habitat du caribou forestier
对驯鹿栖息地上的 tordeuse des bourgeons de läpinette (TBE) 和 thuringiensis ssp kurstaki (Btk) 的影响
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    2022
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    Alexander Graham Bell Canada Graduate Scholarships - Master's
Homotopy Theory of Foliations and Diffeomorphism Groups
叶状结构和微分同胚群的同伦理论
  • 批准号:
    2113828
  • 财政年份:
    2021
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Integral Subvarieties for Foliations on Shimura Varieties in Positive Characterstic.
志村品种正面性状叶的完整亚品种。
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    546746-2020
  • 财政年份:
    2021
  • 资助金额:
    --
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
New studies of foliations and dynamical systems, and their applications
叶状结构和动力系统的新研究及其应用
  • 批准号:
    21H00980
  • 财政年份:
    2021
  • 资助金额:
    --
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
CAREER: Singular Riemannian Foliations and Applications to Curvature and Invariant Theory
职业:奇异黎曼叶状结构及其在曲率和不变理论中的应用
  • 批准号:
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  • 财政年份:
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  • 资助金额:
    --
  • 项目类别:
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Taut foliations, representations, and the computational complexity of knot genus
结属的拉紧叶状、表示和计算复杂性
  • 批准号:
    EP/T016582/2
  • 财政年份:
    2021
  • 资助金额:
    --
  • 项目类别:
    Fellowship
Conformal Symplectic Structures, Contact Structures, Foliations, and Their Interactions
共形辛结构、接触结构、叶状结构及其相互作用
  • 批准号:
    2104473
  • 财政年份:
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