This book provides an account of some of the research work of the author on the Morse's critical point theory and its application to the famous unsolved Poincare conjecture. It is also devoted to some of the most important developments in this subject achieved by several outstanding mathematicians during the last 50 years with more emphasis on recent results.
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ISBN-13
978-9971-5-0977-4 (9789971509774)
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Schweitzer Klassifikation
Autor*in
The American College of Greece
The Morse-Smale characteristic of a differentiable manifold; Heegaard splittings of manifolds and the Poincare conjecture; handle decompositions of manifolds; covering of differentiable manifolds with open disks; on the monotone union and monotone intersection properties of topological manifolds; Morse Smale inequalities for a vector field on a manifold; gradient vector fields; generalized Poincare conjecture in dimensions greater than four; differentiable and combinational structures on manifolds; on the structure of differentiable manifolds; the h-Cobordism and s-Cobordism theorems; on the topology of four-dimensional manifolds; on a conjecture of Rene Thom in critical point theory; applications of Morse theory to differential equations and calculus of variations; research problems.
