Low-dimensional topology and geometry Robion C. Kirby1 Department of Mathematics, University of California, Berkeley, CA 94720 A t the core of low-dimensional topology has been the classi?ca-tion of knots and links in the 3-sphere and the classi?cation of 3- and 4-dimensional manifolds (see Wikipedia for the de?nitions of basic to Excellent introduction to the subject of low-dimensional geometry. I read this book as a warm-up for more advanced topics (algebraic topology, hyperbolic knot theory) and was not disappointed. This book is aimed at advanced undergraduates, but in reality if one has had a good semester of analysis and algebra this book should be very understandable. Her research is in low-dimensional topology, which means that she gets to work with tangles and knots both in Mathematics and in her knitting. Before coming to Ohio State, she earned her undergraduate degree from Miami University, and then earned her Ph.D. at Ohio State. Jenny George is currently the head instructor for Calculus One. The American Mathematical Society recently published Braid Foliations in Low-Dimensional Topology, co-authored by UB Mathematics Professor William W. Menasco, and Western Illinois University Professor Douglas J. LaFountain.This book is a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more Thank you for your interest in our Low Dimensional Topology Workshop. I hope you will consider attending other workshops here in the near future. In recent years, there has been lots of exciting progress in many branches of low-dimensional topology, including Heegard Floer and Khovanov Homology, small 4-Manifolds, TQFT, knot concordance and Higher-dimensional knots are n-dimensional spheres in m-dimensional Euclidean space. High-dimensional geometric topology. In high-dimensional topology, characteristic classes are a basic invariant, and surgery theory is a key theory. A characteristic class is a way of associating to each principal bundle on a topological space X a cohomology Dimensional Topology, and various others. The usual topology course offered at Geneseo is General Topology (Math 338), which has its foundation in set theory, and this course will be significantly different from it. This course is an introduction to some topics in low-dimensional, geometric topology, and algebraic topology, including knots and Differential Geometric Methods in Low-dimensional Topology S. K. Donaldson July 9, 2008 1 Introduction This is a survey of various applications of analytical and geometric techniques to problems in manifold topology. The author has been involved in only some of these developments, but it seems more illuminating not to confine the discussion to The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology Banff International Research Center, Banff, Canada, March 2019. Surgery on links and the Heegaard Floer d-invariant, PDF Winter Meeting of the Canadian Mathematical Society, Session on Topology, Vancouver BC, December 2018 Thurston's Three-Dimensional Geometry and Topology, Vol. 1 (Princeton University Press, 1997) is a considerable expansion of the ?rst few chapters of these notes. Later chapters have not yet appeared in book form. Please send corrections to Silvio Levy at levy@msri.org. set topology, which is concerned with the more