The study of the mapping class group Mod(S) is a classical topic that experiences a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem.
Suitable for those seeking to familiarize themselves with research in braid groups, configuration spaces and their applications. This title takes the reader through the fundamental theory and on to research and applications in the fields such as astrophysics, cryptography and robotics.
Offers a review of the basic concepts and terminologies of geometric knots such as the thickness of a knot and the rope length of a knot. This book covers topics such as the global minimum rope length of knots, and various lower and upper rope length bounds of knots in terms of their crossing numbers.
Consists of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. This book contains lectures on the many aspects of applications of knot theory. It gives an in-depth survey of the advances of knot theory and its applications.
The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. This book deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra.
Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.
This volume offers a thorough introduction to K-theory, both algebraic and topological, and to current research topics including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the K-theory of schemes, the theory of dg-categories, and more.