Complexes in low-dimensional topology

低维拓扑中的复形

• 批准号: 0905798
• 负责人: Jennifer Schultens
• 金额: $ 21.74万
• 依托单位: University of California-Davis
• 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: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905798&HistoricalAwards=false
• 关键词: Complexes; low; dimensional; topology

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).In "3-manifolds as viewed from the curve complex" John Hempel illustrated the utility of the curve complex as a tool for understanding 3-manifolds.His work introduced the techniques used in geometric group theory into the study of low-dimensional manifolds. The Gromov hyperbolicity of the curve complex, established by Howard Masur and Yair Minsky, provides deep insights into the structure of the complex and the information it encodes. The fanstastic work of Hossein Namazi, Saul Schleimer and Juan Souto deserves particular mention in this context. In recent years, the P.I. has studied several complexes, in particular the width complex (defined by the P.I.) and the Kakimizu complex. These complexes shed light on many of the P.I.'s pet problems on genus, rank and stabilization of Heegaard splittings.The P.I. pursues research in the area of low-dimensional topology, specifically 3-manifolds. The project builds on the cross-fertilization of low-dimensional topology and geometric group theory. The P.I. maintains several national and international collaborations with mathematicians in the United States, Germany and Israel. The P.I. aims to involve graduate and undergraduate students in some aspects of the project.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。在“从曲线复合体看3-流形”一文中，John Hempel说明了曲线复合体作为理解3-流形的工具的效用。他的工作将几何群论中的技术引入到低维流形的研究中。由Howard Masur和Yair Minsky建立的曲线复合体的Gromov双曲性为复合体的结构及其编码的信息提供了深刻的见解。在这方面，侯赛因·纳马齐、索尔·施莱默和胡安·索托的杰出作品值得特别提及。近年来，P.I.研究了几种配合物，特别是宽度配合物（由P.I.定义）和Kakimizu配合物。这些综合体揭示了许多P.I.在属、阶和稳定性方面的宠物问题。P.I.从事低维拓扑领域的研究，特别是3-流形。该项目建立在低维拓扑学和几何群论相互作用的基础上。P.I.与美国、德国和以色列的数学家保持着几项国内和国际合作。P.I.的目的是让研究生和本科生参与项目的某些方面。