Algebraic and Geometric Topology

代数和几何拓扑

• 批准号: 9802386
• 负责人: William Dwyer
• 金额: $ 29.48万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802386&HistoricalAwards=false
• 关键词: Algebraic; Geometric; Topology

9802386Dwyer The investigators are working on a number of problems from algebraicand geometric topology. Dwyer is extending earlier research on thehomotopy theory of topological groups and on the relationship betweenalgebraic K-theory and number theory. Taylor is studying smooth4-manifolds, looking into some algebraic results at the heart ofgeometric topology and developing applications of controlled topologyto stratified spaces. Williams is concentrating on Reimann-RochTheorems in differential topology, in particular, by generalizing thesetheorems to related theories and finding applications of them tostratified spaces and to curvature questions. The researchers in this project are concerned with geometry, bothwith the behavior of visible shapes and the more mysterious qualitiesof higher dimensional configurations. They work on developingtechniques for making spatial calculations, and also on findinginstances in which simple geometrical ideas can clarify other kinds ofmathematics. Some of the specific questions the investigators studyare quite complex, but the fundamental goal of the field of topologyin which they are involved goes back to the Greeks: it is tounderstand better the relationship between number and shape, betweenquantities that can be manipulated by calculation and the moreelusive spatial forms (of all dimensions) that arise repeatedly inmathematics and other sciences.***

9802386Dwyer 研究人员正在研究代数和几何拓扑中的许多问题。 Dwyer 正在扩展拓扑群同伦理论以及代数 K 理论与数论之间关系的早期研究。 泰勒正在研究平滑 4 流形，研究几何拓扑核心的一些代数结果，并开发受控拓扑在分层空间中的应用。 威廉姆斯专注于微分拓扑中的赖曼-罗赫定理，特别是通过将这些定理推​​广到相关理论并找到它们在分层空间和曲率问题上的应用。 该项目的研究人员关注几何学，包括可见形状的行为和高维结构的更神秘的品质。 他们致力于开发空间计算技术，并寻找简单的几何思想可以阐明其他类型数学的实例。 研究人员研究的一些具体问题相当复杂，但他们所涉及的拓扑学领域的基本目标可以追溯到希腊人：更好地理解数字和形状之间的关系，可以通过计算操纵的数量之间的关系，以及在数学和其他科学中反复出现的更难以捉摸的空间形式（所有维度）之间的关系。***