Showing papers in "Bulletin of The London Mathematical Society in 1987"

From Groups to Groupoids: a Brief Survey

Abstract: A groupoid should be thought of as a group with many objects, or with many identities. A precise definition is given below. A groupoid with one object is essentially just a group. So the notion of groupoid is an extension of that of groups. It gives an additional convenience, flexibility and range of applications, so that even for purely group-theoretical work, it can be useful to take a path through the world of groupoids. A succinct definition is that a groupoid G is a small category in which every morphism is an isomorphism. Thus G has a set of morphisms, which we shall call just elements of G, a set Ob(G) of objects or vertices, together with functions s, t : G→ Ob(G), i : Ob(G) → G such that si = ti = 1. The functions s, t are sometimes called the source and target maps respectively. If a,b ∈ G and ta = sb, then a product or composite ab exists such that s(ab) = sa, t(ab) = tb. Further, this product is associative; the elements ix, x ∈ Ob(J), act as identities; and each element a has an inverse a with s(a) = ta, t(a) = sa,aa = isa,aaa = ita. An element a is often written as an arrow a : sa→ ta.

MINIMAX METHODS IN CRITICAL POINT THEORY WITH APPLICATIONS TO DIFFERENTIAL EQUATIONS (CBMS Regional Conference Series in Mathematics 65)

Abstract: Discrete and Continuous Dynamical SystemsMinimax Methods in Critical Point Theory with Applications to Differential EquationsAnnales Polonici MathematiciDissertation Abstracts InternationalCritical Point Theorems and Applications to Differential EquationsDifferential and Integral EquationsAnnals of Differential EquationsMinimax Systems and Critical Point TheoryJournal of the Korean Mathematical SocietyAn Introduction to Minimax Theorems and Their Applications to Differential EquationsNonlinearitySign-Changing Critical Point TheoryActa Universitatis CarolinaeVariational Methods in Nonlinear AnalysisTopological Methods in Nonlinear AnalysisHouston Journal of MathematicsLecture Notes in Contemporary Mathematics: 1991Advances in Differential EquationsProceedings of 23rd Conference on Geometry and TopologyMinimax Methods in Critical Point Theory with Applications to Differential Equations. Expository Lectures from the Cbm Regional Conference Held at the University of Miami, January 9-13, 1984Mathematical ReviewsPfahlgründungenStudia Universitatis Babeș-BolyaiTopological Methods in Differential Equations and InclusionsMinimax Theorems and Qualitative Properties of the Solutions of Hemivariational InequalitiesAnalele științifice ale Universității \"Al. I. Cuza\" din IașiStudia Universitatis Babes-B̦olyaiCritical Point Theory and Its ApplicationsCritical Point Theory and Hamiltonian SystemsRCMSome Minimax Theorems and Applications to Nonlinear Partial Differential EquationsEquadiff 7SIAM Journal on Scientific ComputingDel Pezzo Surfaces of Degree FourCommunications in Applied AnalysisSome Aspects of Critical Point TheoryMinimax Methods for Finding Multiple Saddle Critical Points in Banach Spaces and Their ApplicationsTopics in Critical Point TheoryAnnales de la faculté des sciences de ToulouseCritical Point Theory and Its Applications

Immersions and Embeddings of Totally Geodesic Surfaces

Abstract: The work of Waldhausen, Thurston and others has shown that the existence of an embedding of a closed, orientable, incompressible surface in a 3-manifold is a great help in the understanding of that manifold. Unfortunately many examples exist of manifolds which contain no such embedding. However, it does seem at least conjecturally possible that any irreducible manifold with infinite fundamental group could contain an immersion of such a surface, and this has motivated the study of the question of whether such a surface can always be lifted to an embedding in some finite covering of the 3-manifold. The general question seems to be some way from resolution; the purpose of this note is to give an affirmative answer in a very special case.