Algebraic and Geometric Topology
代数和几何拓扑
基本信息
- 批准号:0808659
- 负责人:
- 金额:$ 14.95万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-06-15 至 2012-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
There are a web of conjectures about the surgery theoretic classification of high-dimensional manifolds, culminating in the Farrell-Jones Conjectures in K- and L-theory. The conjectures are closely related to splitting manifolds along codimension one submanifolds. This splitting problem is in turn related to nil groups in algebraic K- and L-theory. This project has several different aspects. One is to solve the connected sum problem -- when is a manifold which is homotopy equivalent to a connected sum itself a connected sum? Another is to provide a strengthening of the Farrell- Jones Conjecture in L-theory, similar to that achieved by Davis-Khan- Ranicki in K-theory. Yet another is to classify involutions on a torus, using the computation of the L-theory of the infinite dihedral group and the proof of the Farrell-Jones Conjecture in L-theory for crystallographic groups, joint with Connolly. There are some middle and low dimensions problems too, involving mapping tori of self- homotopy equivalences of lens spaces and a certain aspect of link concordance.The goal, as usual in geometric topology, is to use a variety of algebraic, geometric, and analytic techniques to find and compute invariants for classification. Geometric topology is the study of manifolds. An n-dimensional manifold is a set of points locally modeled on n-dimensional Euclidean space. For instance, a 2-manifold is a surface and looks like a plane near each point. Many physical phenomenon are represented by manifolds, and as such, understanding the global structure of a manifold, and what possible manifolds exist, is fundamental to the sciences, as well as to mathematics. Manifold theory connects with most areas of mathematics, as well as with physical phenomena such as cosmology, string theory, and classical and quantum mechanics.
关于高维歧管的手术理论分类,有一个猜想的网络,最终在K-和L理论的Farrell-Jones猜想中达到了最终。 这些猜想与沿着沿着一个子序列的分裂歧管密切相关。 这个分裂问题又与代数K和L理论中的零组有关。 该项目有几个不同的方面。 一种是解决连接的总和问题 - 何时是同型等同于连接总和本身的歧管? 另一个是在L理论中加强Farrell-Jones的猜想,类似于Davis-Khan-Ranicki在K理论中所实现的。 另一个是,使用无限二面基团的L理论和与Connolly关节的L理论中的Farrell-Jones猜想的证据,并证明了Farrell-Jones的猜想的证明,将其分类。 也存在一些中层和低维问题,涉及镜头空间的自相同等效的映射摩托图和链接一致性的某些方面。与几何拓扑相像,该目标是使用各种代数,几何学和分析技术来查找和计算不可传剂进行分类。几何拓扑是对流形的研究。 N维歧管是一组在N维欧几里得空间上进行局部建模的点。例如,一个2个manifold是一个表面,看起来像每个点附近的平面。许多物理现象以多种形式表示,因此,了解流形的全球结构以及存在的歧管,对科学以及数学的基础是基础。 歧管理论与数学的大多数领域以及诸如宇宙学,弦理论以及经典和量子力学等物理现象相关。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

暂无数据
数据更新时间:2024-06-01
James Davis其他文献
A sketching interface for articulated figure animation
用于铰接图形动画的草图界面
- DOI:10.1145/1281500.128153410.1145/1281500.1281534
- 发表时间:20072007
- 期刊:
- 影响因子:0
- 作者:James Davis;Maneesh Agrawala;Erika Chuang;Zoran Popovic;David SalesinJames Davis;Maneesh Agrawala;Erika Chuang;Zoran Popovic;David Salesin
- 通讯作者:David SalesinDavid Salesin
Key neurochemical markers for the prevention of suicide
预防自杀的关键神经化学标志物
- DOI:10.1016/j.trac.2009.06.00210.1016/j.trac.2009.06.002
- 发表时间:20092009
- 期刊:
- 影响因子:0
- 作者:S. Slater;M. M. Villalba;James DavisS. Slater;M. M. Villalba;James Davis
- 通讯作者:James DavisJames Davis
Design of a smart sensor mesh for the measurement of pH in ostomy applications
用于测量造口术应用中 pH 值的智能传感器网的设计
- DOI:10.1007/s10853-019-03600-x10.1007/s10853-019-03600-x
- 发表时间:20192019
- 期刊:
- 影响因子:4.5
- 作者:A. McLister;Charnete Casimero;Aaron McConville;Charlotte M. Taylor;Clare L. Lawrence;Robert B. Smith;A. Mathur;James DavisA. McLister;Charnete Casimero;Aaron McConville;Charlotte M. Taylor;Clare L. Lawrence;Robert B. Smith;A. Mathur;James Davis
- 通讯作者:James DavisJames Davis
Drinking water treatment by multistage filtration on a household scale: Efficiency and challenges.
家庭规模的多级过滤饮用水处理:效率和挑战。
- DOI:10.1016/j.watres.2020.11581610.1016/j.watres.2020.115816
- 发表时间:20202020
- 期刊:
- 影响因子:12.8
- 作者:R. C. Medeiros;N. D. M. N. Fava;B. Freitas;L. P. Sabogal;M. Hoffmann;James Davis;P. Fernández;J. ByrneR. C. Medeiros;N. D. M. N. Fava;B. Freitas;L. P. Sabogal;M. Hoffmann;James Davis;P. Fernández;J. Byrne
- 通讯作者:J. ByrneJ. Byrne
Gradient domain HDR compositing
梯度域HDR合成
- DOI:10.1145/2037715.203775510.1145/2037715.2037755
- 发表时间:20112011
- 期刊:
- 影响因子:0
- 作者:Oliver Wang;James DavisOliver Wang;James Davis
- 通讯作者:James DavisJames Davis
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James Davis的其他基金
Workshops on Smart Manufacturing with Open and Scaled Data Sharing in Semiconductor and Microelectronics Manufacturing; Virtual and In-Person; Washington, DC; October/November 2023
半导体和微电子制造中开放和规模化数据共享的智能制造研讨会;
- 批准号:23345902334590
- 财政年份:2023
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
MICA: Stomasense: A New Route to the Proactive Detection and Management of Leaks within Ostomy Pouches
MICA:Stomasense:主动检测和管理造口袋内泄漏的新途径
- 批准号:MR/W029561/1MR/W029561/1
- 财政年份:2023
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Research GrantResearch Grant
Collaborative Research: SaTC: CORE: Small: Improving Sanitization and Avoiding Denial of Service Through Correct and Safe Regexes
协作研究:SaTC:核心:小型:通过正确和安全的正则表达式改进清理并避免拒绝服务
- 批准号:21351562135156
- 财政年份:2022
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Symposium on the Strategy for Resilient Manufacturing Ecosystems through AI
通过人工智能打造弹性制造生态系统战略研讨会
- 批准号:21320672132067
- 财政年份:2021
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
CAS: Collaborative Research: Boronium Ionic Liquids - Impact of Structure on Chemistry, Electrochemical Stability, Ion Dynamics, and Charge Transport
CAS:合作研究:硼离子液体 - 结构对化学、电化学稳定性、离子动力学和电荷传输的影响
- 批准号:21029782102978
- 财政年份:2021
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Workshop: Aligning AI and U.S. Advanced Manufacturing Competitiveness
研讨会:人工智能与美国先进制造业竞争力的结合
- 批准号:20496702049670
- 财政年份:2020
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Finite Fields and their Applications at Simon Fraser University
西蒙弗雷泽大学的有限域及其应用
- 批准号:19050241905024
- 财政年份:2019
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Topology of Manifolds: Interactions between High and Low Dimensions
流形拓扑:高维和低维之间的相互作用
- 批准号:18506201850620
- 财政年份:2019
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Ionic and Molecular Materials of High Thermal Stability: Design, Structure, and Function
高热稳定性离子和分子材料:设计、结构和功能
- 批准号:18001221800122
- 财政年份:2018
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
Summer School on Surgery and the Classification of Manifolds
外科和歧管分类暑期学校
- 批准号:16384641638464
- 财政年份:2016
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Standard GrantStandard Grant
相似国自然基金
低维流形的代数、几何与拓扑
- 批准号:12171092
- 批准年份:2021
- 资助金额:50 万元
- 项目类别:面上项目
代数拓扑中的代数几何与数论方法
- 批准号:11701263
- 批准年份:2017
- 资助金额:19.0 万元
- 项目类别:青年科学基金项目
基于几何代数的动态拓扑关系表达与自适应计算模型
- 批准号:41601417
- 批准年份:2016
- 资助金额:25.0 万元
- 项目类别:青年科学基金项目
结构空间与代数簇的几何拓扑
- 批准号:11671286
- 批准年份:2016
- 资助金额:48.0 万元
- 项目类别:面上项目
代数几何与拓扑的交叉
- 批准号:11671222
- 批准年份:2016
- 资助金额:48.0 万元
- 项目类别:面上项目
相似海外基金
RTG: Algebraic and Geometric Topology at Michigan State
RTG:密歇根州立大学的代数和几何拓扑
- 批准号:21359602135960
- 财政年份:2022
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Continuing GrantContinuing Grant
Algebraic and Geometric Topology In Dimensions Three and Four
三维和四维的代数和几何拓扑
- 批准号:22671242267124
- 财政年份:2019
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:StudentshipStudentship
Theory and applications of Stone-duality for quasi-Polish spaces
准波兰空间的石对偶性理论与应用
- 批准号:18K1116618K11166
- 财政年份:2018
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Grant-in-Aid for Scientific Research (C)Grant-in-Aid for Scientific Research (C)
Innovative research of geometric topology and singularities of differentiable mappings
几何拓扑和可微映射奇异性的创新研究
- 批准号:17H0612817H06128
- 财政年份:2017
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Grant-in-Aid for Scientific Research (S)Grant-in-Aid for Scientific Research (S)
Problems in Geometric, Algebraic and Quantitative Topology
几何、代数和定量拓扑问题
- 批准号:15101781510178
- 财政年份:2015
- 资助金额:$ 14.95万$ 14.95万
- 项目类别:Continuing GrantContinuing Grant