International Seminar on Low-Dimensional Homotopy Theory and Combinatorial Group Theory

低维同伦理论与组合群论国际研讨会

• 批准号: 0918418
• 负责人: F Rudolf Beyl
• 金额: $ 2.03万
• 依托单位: Portland State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0918418&HistoricalAwards=false
• 关键词: International; Seminar; Low; Dimensional; Homotopy

Topologists will meet for an intensive international workshop at Wallowa Lake Lodge in Oregon. The focus of this meeting will be ongoing work on unsolved problems in low-dimensional homotopy theory and combinatorial group theory. These include Whitehead's Asphericity Conjecture, the Andrews-Curtis Conjecture, Wall's Domination Problem in dimension two, the relation gap problem, and the Eilenberg-Ganea Conjecture. They highlight the very delicate interplay of topology and group theory in low-dimensional homotopy theory and also involve other branches of mathematics like geometry, combinatorics, and algebraic K-theory.This workshop is in succession to similar conferences held in Italy, the Pacific Northwest, and Russia. It aims to maintain needed connections between American and international topologists. The problems to be addressed are geometric in nature, challenging the basic human conception of what three-dimensional space is or can be thought to be. Improvements in the understanding of the topics and problems considered at the seminar may open new avenues of thinking and modelling in topology and eventually in the natural sciences. The workshop format emphasizes detailed discussion of ideas in progress and collaboration of the participants, from graduate students to early-career researchers to senior experts.

拓扑学家们将在俄勒冈州的瓦洛瓦湖小屋举行一次密集的国际研讨会。 本次会议的重点将是正在进行的工作，在低维同伦理论和组合群论未解决的问题。 其中包括怀特海的非球面猜想、安德鲁斯-柯蒂斯猜想、沃尔在二维空间的支配问题、关系缺口问题和艾伦伯格-加内亚猜想。 他们突出了拓扑和群论在低维同伦理论中非常微妙的相互作用，也涉及其他数学分支，如几何，组合学和代数K理论。这个研讨会是在继承类似的会议在意大利，太平洋西北地区，俄罗斯举行。 它旨在保持美国和国际拓扑学家之间的必要联系。 要解决的问题是几何的性质，挑战什么是三维空间或可以被认为是人类的基本概念。 在研讨会上审议的主题和问题的理解的改进可能会开辟新的途径的思维和建模拓扑学，并最终在自然科学。 研讨会的形式强调详细讨论进展中的想法和参与者的合作，从研究生到早期职业研究人员到高级专家。