Lower K- and L-theory
by Andrew Ranicki
Publisher: Cambridge University Press 2001
Number of pages: 177
This is the first treatment in book form of the applications of the lower K- and L-groups (which are the components of the Grothendieck groups of modules and quadratic forms over polynomial extension rings) to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. The author uses only elementary constructions and gives a full algebraic account of the groups involved.
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by R. Fenn, D.P. Ilyutko, L.H. Kauffman, V.O. Manturov - arXiv
The purpose of this paper is to give an introduction to virtual knot theory and to record a collection of research problems that the authors have found fascinating. The paper introduces the theory and discusses some problems in that context.
by S. Hong, J. Kalliongis, D. McCullough, J. H. Rubinstein - arXiv
The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature. For any elliptic 3-manifold M, the inclusion from the isometry group of M to the diffeomorphism group of M is a homotopy equivalence.
by M. Boittin, E. Callahan, D. Goldberg, J. Remes - Ohio State University
This is an innovative project by a group of Yale undergraduates: A Multi-Disciplinary Exploration of Non-Orientable Surfaces. The course is designed to be included as a short segment in a late middle school or early high school math course.
by Benson Farb, Dan Margalit - Princeton University Press
Our goal in this book is to explain as many important theorems, examples, and techniques as possible, as quickly and directly as possible, while at the same time giving (nearly) full details and keeping the text (nearly) selfcontained.