2012 Redbud Geometry/Topology Conference

2012年紫荆花几何/拓扑会议

• 批准号: 1148724
• 负责人: Jesse Johnson
• 金额: $ 2.56万
• 依托单位: Oklahoma State University
• 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: 2011-11-15 至 2013-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1148724&HistoricalAwards=false
• 关键词: 2012; Redbud; Geometry; Topology; Conference

This conference will feature a number of talks by Tao Li and by other experts on Heegaard splittings and ranks of fundamental groups. A Heegaard splitting is a decomposition of a 3-dimensional manifold into two simple pieces called handlebodies along a surface. A Heegaard splitting defines a presentation for the fundamental group of the 3-manifold in which the number of generators is equal to the genus of the surface. Thus the rank of the 3-manifold (the minimal number of generators) is less than or equal to the genus of the minimal Heegaard surface. In most cases, rank and genus are equal, but a small number of examples have been found in which the rank is strictly less than the genus. Tao Li recently discovered the first examples of hyperbolic 3-manifolds with rank strictly less than genus. This raises the question of how common these examples are and how big the difference between rank and genus can be.When we look at the surface of the earth from ground level, it appears to be a flat plane that goes on forever in all directions. However, from world navigation and viewing the earth from space, we know that it is, in fact, a completely different shape - a sphere, or the surface of a ball. Similarly, the universe that we live in appears to be a flat 3-dimensional space that goes on forever in all directions. Unfortunately we have no way of checking what the shape actually is, but we can study the possible shapes that it could be. This is the focus of 3-dimensional topology. This conference will bring together experts from around the world to discuss recent developments at the interface between algebraic methods and geometric methods for studying 3-dimensional spaces.http://comp.uark.edu/~matthewd/redbud/http://www.math.okstate.edu/~jjohnson/redbud/

这次会议将由陶力和其他专家就希加德的分裂和基本集团的队伍作一系列报告。Heegaard分裂是将三维流形沿着曲面分解成两个简单的称为手柄的部分。Heegaard分裂定义了生成元数等于曲面亏格的3-流形的基本群的表示。因此，3-流形(生成元的最小数目)的秩小于或等于极小Heegaard曲面的亏格。在大多数情况下，等级和亏格是相等的，但也有少数例子表明，等级严格小于亏格。陶力最近发现了第一批秩严格小于亏格的双曲3-流形。这就提出了这样一个问题：这些例子有多常见，等级和属之间的差别有多大。当我们从地面上看地球表面时，它似乎是一个永远向四面八方延伸的平面。然而，从世界导航和从太空观看地球，我们知道它实际上是一个完全不同的形状-球体，或球的表面。同样，我们生活的宇宙似乎是一个平坦的三维空间，向各个方向永无止境。不幸的是，我们无法检查它的实际形状，但我们可以研究它可能的形状。这是三维拓扑学研究的重点。这次会议将汇集来自世界各地的专家，讨论在研究三维spaces.http://comp.uark.edu/~matthewd/redbud/http://www.math.okstate.edu/~jjohnson/redbud/的代数方法和几何方法之间的接口的最新进展。