Contact manifolds and Heegaard Floer homology

接触流形和 Heegaard Florer 同源性

基本信息

  • 批准号:
    1104690
  • 负责人:
  • 金额:
    $ 12.63万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2011
  • 资助国家:
    美国
  • 起止时间:
    2011-06-01 至 2015-05-31
  • 项目状态:
    已结题

项目摘要

The proposed project is devoted to deepen the connection of two seemingly different subfields of low dimensional topology, namely contact topology and Heegaard Floer homologies. The invariants of Legendrian knots in Heegaard Floer homology gave several first proofs of new phenomenons in knot theory. During this project the PI would like to understand relations between the already defined knot invariants for Legendrian knots, see how these invariants are related for concordant Legendrian knots and use these invariants together with other tools to distinguish and hopefully classify Legendrian representations of a wide class of knots. Contact geometry provided a tool for proving results in Heegaard Floer homology. As part of the proposed projects the PI would like to use tools from contact geometry to give a lower bound for the rank of Heegaard Floer homology for a manifold that contains an incompressible surface.Low dimensional topology describes our physical world; the space we live in is a 3-dimensional manifold while space-time is a 4-dimensional manifold. The proposed project is aimed to deepen the connection between two subfields of low dimensional topology that are inspired by physics in different ways. The first is the theory of contact manifolds, which arise quite naturally as phase spaces of moving objects. The other is Heegaard Floer homology which is obtained by associating to an object a configuration space of constrained functions and computing the space's algebro-topological invariants.
拟议的项目是致力于深化低维拓扑,即接触拓扑和Heegaard Floer同调的两个看似不同的子领域的连接。在Heegaard Floer同调中Legendrian纽结的不变量给出了纽结理论中新现象的几个初步证明。在本项目中,PI希望了解已定义的勒让德结的结不变量之间的关系,了解这些不变量如何与一致的勒让德结相关,并将这些不变量与其他工具一起使用,以区分并有望对广泛类别的勒让德结表示进行分类。接触几何提供了一个工具,证明结果Heegaard Floer同源。作为项目的一部分,PI希望使用接触几何的工具来给出一个包含不可压缩曲面的流形的Heegaard Floer同调秩的下界。低维拓扑描述了我们的物理世界;我们生活的空间是一个3维流形,而时空是一个4维流形。该项目旨在加深低维拓扑的两个子领域之间的联系,这两个子领域以不同的方式受到物理学的启发。第一个是接触流形的理论,它很自然地出现在运动物体的相空间中。另一个是Heegaard Floer同调,它是通过将一个对象与一个约束函数的构形空间相关联并计算该空间的代数拓扑不变量而得到的。

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)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Katrin Wehrheim其他文献

L2-Topology and Lagrangians in the Space of Connections Over a Riemann Surface
  • DOI:
    10.1007/s00039-010-0086-3
  • 发表时间:
    2010-09-02
  • 期刊:
  • 影响因子:
    2.500
  • 作者:
    Tomasz S. Mrowka;Katrin Wehrheim
  • 通讯作者:
    Katrin Wehrheim

Katrin Wehrheim的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Katrin Wehrheim', 18)}}的其他基金

Connections between Symplectic and Low Dimensional Topology
辛和低维拓扑之间的联系
  • 批准号:
    1708916
  • 财政年份:
    2017
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
Pseudoholomorphic Curves in Topology and Symplectic Geometry
拓扑和辛几何中的伪全纯曲线
  • 批准号:
    1442345
  • 财政年份:
    2014
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Pseudoholomorphic Curves in Topology and Symplectic Geometry
拓扑和辛几何中的伪全纯曲线
  • 批准号:
    1308684
  • 财政年份:
    2013
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
CAREER: The symplectic category, Floer field theory, and relations to gauge theory and topology
职业:辛范畴、弗洛尔场论以及与规范理论和拓扑的关系
  • 批准号:
    0844188
  • 财政年份:
    2009
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
Floer theories in symplectic geometry and low dimensional topology
辛几何和低维拓扑中的弗洛尔理论
  • 批准号:
    0706967
  • 财政年份:
    2007
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Instanton Floer Homology with Lagrangian Boundary Conditions and the Atiyah-Floer Conjecture
具有拉格朗日边界条件的 Instanton Floer 同调和 Atiyah-Floer 猜想
  • 批准号:
    0636580
  • 财政年份:
    2006
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
Instanton Floer Homology with Lagrangian Boundary Conditions and the Atiyah-Floer Conjecture
具有拉格朗日边界条件的 Instanton Floer 同调和 Atiyah-Floer 猜想
  • 批准号:
    0405647
  • 财政年份:
    2004
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant

相似海外基金

Research on 3-manifolds and links based on the Heegaard theory
基于Heegaard理论的3流形与连杆研究
  • 批准号:
    21K20328
  • 财政年份:
    2021
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Grant-in-Aid for Research Activity Start-up
Smooth 4-Manifold Topology, 3-Manifold Group Actions, the Heegaard Tree, and Low Volume Hyperbolic 3-Manifolds
平滑 4 流形拓扑、3 流形组动作、Heegaard 树和低容量双曲 3 流形
  • 批准号:
    2003892
  • 财政年份:
    2020
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Three-Dimensional Manifolds, Heegaard Floer Homology and Knot Theory
三维流形、Heegaard Floer 同调和纽结理论
  • 批准号:
    1904628
  • 财政年份:
    2019
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Heegaard Splitting and Topology of 3-Manifolds
三流形的 Heegaard 分裂和拓扑
  • 批准号:
    1906235
  • 财政年份:
    2019
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Degree-One Maps, Surgery, and Heegaard Genus of 3-Manifolds
一阶映射、手术和 3 流形的 Heegaard 属
  • 批准号:
    1607830
  • 财政年份:
    2016
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
Heegaard splitting of 3-manifolds
3 流形的 Heegaard 分裂
  • 批准号:
    1305613
  • 财政年份:
    2013
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
Research on distances of Heegaard splittings of 3-manifolds and bridge splittings of links
三流道Heegaard分裂距离及连杆桥分裂的研究
  • 批准号:
    25887039
  • 财政年份:
    2013
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Grant-in-Aid for Research Activity Start-up
Heegaard Floer homology, knots, and three-manifolds
Heegaard Floer 同调、结和三流形
  • 批准号:
    1309152
  • 财政年份:
    2013
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Continuing Grant
3-Manifolds: Heegaard Splittings, the Curve Complex, and Hyperbolic Geometry
3-流形:Heegaard 分裂、复合曲线和双曲几何
  • 批准号:
    1308209
  • 财政年份:
    2013
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
Heegaard Splittings, Knots and 3-Manifolds
Heegaard 分裂、结和 3 流形
  • 批准号:
    1207765
  • 财政年份:
    2012
  • 资助金额:
    $ 12.63万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了