Differential Topology: An Introduction
Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.
This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.
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axis basis calculus Chap chapter chart U,o circle class Cr closed compact manifold components connecting surgery constructed continuous function Corollary cosh critical level defined Definition Let denote diffeomorphism differentiable function differentiable manifold differential structure disconnecting surgery domain embed embedding euclidean space example Exercise FIGURE finite subcover function f Grad gradientlike vector field handles Hausdorff measure Heine-Borel theorem hence homeomorphic immersion Int B2 integral curves inverse function theorem jacobian matrix Lemma Let f linear manifold with boundary Morse function nearness space nondegenerate critical point nonorientable nonsingular Note obtain open cover open sets open subset orientable surface orientation preserving pair picture point of f Prove rank real numbers regular levels S0 X Int satisfying sinh sphere submanifold subspace Suppose surgery of type surgical descendants tangent vector topological property topological space torus trace twisting surgery vector field verify