Functions on Manifolds: Algebraic and Topological Aspects PDF Download

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Functions on Manifolds: Algebraic and Topological Aspects

Functions on Manifolds: Algebraic and Topological Aspects PDF Author: Vladimir Vasilʹevich Sharko
Publisher: American Mathematical Soc.
ISBN: 9780821845783
Category : Mathematics
Languages : en
Pages : 210

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Book Description
This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.