Algebraic and Geometric Topology

[802386] dwyer研究人员正在研究代数和几何拓扑学中的一些问题。Dwyer对拓扑群的同伦理论和代数k理论与数论之间关系的研究进行了扩展。泰勒正在研究光滑流形，研究几何拓扑核心的一些代数结果，并发展控制拓扑在分层空间中的应用。Williams主要研究微分拓扑学中的reiman - rochtheorem，特别是通过将这些定理推广到相关理论中，并找到它们在分层空间和曲率问题中的应用。这个项目的研究人员关注的是几何，既有可见形状的行为，也有更高维度结构的更神秘的品质。他们致力于发展空间计算的技术，同时也在寻找简单的几何概念可以解释其他类型数学的实例。研究者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：更好地理解数字与形状之间的关系，可以通过计算操纵的数量与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

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.***