Conference at MSRI in Low Dimensional-Topology

小行星9727594 该奖项将提供部分报销的旅费和生活费的发言者和与会者在会议上低维拓扑发生在数学科学研究中心，伯克利，加州，1998年5月22日至26日。 会议的目的是汇集研究人员在所有链的低维拓扑结构，使他们能够获得一个整体的视角在该领域的发展。 近年来，三维、四维流形和纽结理论的研究取得了令人振奋的新进展。 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施肥，使研究生接触到这些思想，并鼓励新的合作。 这次会议是在麻省理工学院一个密切相关的为期一年的项目结束一年后举行的。 因此，很自然地要审查如何在接下来的一年里巩固这一领域的进展，会议的另一个好处是向更广泛的农业界展示这一进展。 大约有150名数学家参加了会议，其中50多名是研究生。 有些讲座是专门为这些学生量身定做的。 拓扑解决了那些只依赖于连续性的几何属性，即，一个点接近另一个点的概念，但忽视了高中几何学中的交易存量，如距离，角度，面积，体积等量的测量。 平面拓扑学在通俗科学文献中常被称为橡皮片几何学，它抓住了这门学科的本质精神，却没有给出拓扑学家可能在他们的科学中使用的技术的任何暗示。 它们面临着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，而在过去的世纪，人们逐渐组装了大量武器来对付这些特性。 低维拓扑，主要是3维和4维几何对象的拓扑，提出了它自己的特殊问题，因为虽然我们有直觉，我们应该能够理解这些对象更容易，生活在3维空间和4维时空，事实上，许多代数机器，已开发的拓扑失败在较低的维度。 近年来，在这方面也取得了一些显著的进展，这也是M.S.R.I.会议的中心主题。在五月。 同样值得注意的是，低维拓扑学已经得到了充分的高度发展，例如，在纽结理论在高分子化学和DNA研究中的应用。 随着这一领域的不断发展，它所处理的对象的直接性很可能导致它的进一步技术进步，在真实的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.***