Conference at MSRI in Low Dimensional-Topology

[9727594]卡森：该奖项将为参加1998年5月22日至26日在加州伯克利数学科学研究中心举行的低维拓扑会议的演讲者和参与者提供部分旅费和生活津贴。会议的目的是将低维拓扑各领域的研究人员聚集在一起，使他们能够获得该领域发展的整体视角。近年来，三维和四维流形和结论的研究取得了令人兴奋的新进展。将这些领域的研究人员聚集在一起，鼓励了思想和技术的交叉交流，让研究生接触到这些思想，并鼓励了新的合作。这次会议是在一个密切相关的为期一年的atm.s.r.i.项目结束一年后举行的。因此，在接下来的一年里，回顾这一领域的进展是如何巩固的是很自然的，会议的另一个好处是向更广泛的数学界展示这一进展。大约150名数学家参加了这次会议，其中50多名是研究生。有些讲座是专门为这些学生量身定制的。拓扑学处理的是那些只依赖于非连续性的几何性质，也就是说，依赖于一个点靠近另一个点的概念，但它忽略了高中几何的库存，诸如距离、角度、面积、体积等量的测量。在通俗的科学文献中，平面的拓扑学通常被称为橡胶板几何，这抓住了这门学科的基本精神，而没有给拓扑学家在他们的科学中可能使用的技术太多的暗示。它们面对的是一些非常基本但难以捉摸的特性，这些特性在刚性被驱除后仍然存在，而在过去的一个世纪里，我们看到了处理这些特性的大量武器的逐渐组装。低维拓扑学，主要是三维和四维几何物体的拓扑学，有其自身的特殊问题，因为当我们在三维空间和四维时空中生活时，我们有一种直觉，认为我们应该能够更容易地理解这些物体，事实上，为拓扑学开发的许多代数机制在这些较低的维度中都失败了。近年来，在这方面也取得了一些显著的进展，这也是今年5月在M.S.R.I.举行的会议的中心主题。同样值得注意的是，低维拓扑学已经发展到非常有用的程度，例如，在软结理论在聚合物化学和DNA研究中的应用。随着这一领域的不断发展，它所处理的对象的即时性不太可能导致其进一步的技术进步，在现实世界中找到同样自然的应用

9727594Casson This award will provide partial reimbursement for travel andsubsistence of speakers and participants in a conference onlow-dimensional topology that took place at the Mathematical SciencesResearch Center, Berkeley, California, May 22-26, 1998. The purpose ofthe conference was to bring together researchers working in all strands oflow-dimensional topology and to enable them to gain an overall perspectiveon developments in the field. Recent years have seen exciting newdevelopments in the study of 3- and 4-dimensional manifolds and knottheory. Bringing researchers in these fields together encouraged across-fertilization of ideas and techniques, exposed graduate studentsto these ideas, and encouraged new collaborations. The conference tookplace one year after the end of a closely related year-long program atM.S.R.I. Thus it was natural to review how progress had beenconsolidated in this area over the ensuing year, and an added benefit ofthe conference was to expose this progress to the wider mathematicalcommunity. Approximately 150 mathematicians attended the conference,more than 50 of them graduate students. Some talks were tailoredspecifically for these students. Topology addresses those geometric properties that depend only oncontinuity, i.e., on the notion of one point being close to another, butdisregards the stock in trade of high school geometry, measurement ofquantities such as distance, angle, area, volume, and so forth. Topologyof the plane is often referred to in popular scientific literature asrubber sheet geometry, and this captures the essential spirit of thediscipline without giving so much as a hint of the techniques topologistsmight use in their science. They confront some very basic but elusiveproperties, those that remain after rigidity has been exorcised, and thepast century has seen the gradual assembly of a considerable arsenal ofweapons for dealing with these properties. Low-dimensional topology,mainly the topology of 3- and 4-dimensional geometric objects, presentsspecial problems of its own, for while we have the intuition that weshould be able to apprehend these object more readily, living as we do in3-dimensional space and 4-dimensional space-time, in fact much of thealgebraic machinery that has been developed for topology fails in theselower dimensions. Recent years have seen some remarkable advances on thisfront too, and this was the central theme of the conference at M.S.R.I. inMay. It is also noteworthy that low-dimensional topology has becomesufficiently highly developed to be useful, for example, in applicationsof knot theory to polymer chemistry and to the study of DNA. As this fieldcontinues to progress, the immediacy of the objects with which it deals islikely to lead its further technical advances to find equally naturalapplications in the real world.***