Topics in Low-Dimensional Topology

Recent success with the four-dimensional Poincar#xE9; conjecture has revived interest in low-dimensional topology, especially the three-dimensional Poincar#xE9; conjecture and other aspects of the problems of classifying three-dimensional manifolds.

These problems have a driving force, and have generated a great body of research, as well as insight.The main topics treated in this book include a paper by V Poenaru on the Poincar#xE9; conjecture and its ramifications, giving an insight into the herculean work of the author on the subject.

Steve Armentrout#x27;s paper on #x201C;Bing#x27;s dogbone space#x201D; belongs to the topics in three-dimensional topology motivated by the Poincar#xE9; conjecture.

S Singh gives a nice synthesis of Armentrout#x27;s work.

Also included in the volume are shorter original papers, dealing with somewhat different aspects of geometry, and dedicated to Armentrout by his colleagues #x2014; Augustin Banyaga (and Jean-Pierre Ezin), David Hurtubise, Hossein Movahedi-Lankarani and Robert Wells.Contents: Mathematics of Steve Armentrout: A Review (S Singh)Bing#x27;s Dogbone Space Is Not Strongly Locally Simply Connected (S Armentrout)A Program for the Poincar#xE9; Conjecture and Some of Its Ramifications (V Po#xE9;naru)On the Foundation of Geometry, Analysis, and the Differentiable Structure for Manifolds (D Sullivan)A Conformal Invariant Characterizing the Sphere (A Banyaga #x26; J-P Ezin)Spaces of Holomorphic Maps from #x2200;P1 to Complex Grassmann Manifolds (D E Hurtubise)Sets with Lie Isometry Groups (H Movahedi-Lankarani #x26; R Wells)Readership: Researchers in mathematics and physics.