Differential Topology Books Download

This note explains how two standard techniques from the study of smooth manifolds, Morse theory and Bochner�s method, can be adapted to aid in the investigation of combinatorial spaces.

This note covers the following topics: Smooth manifolds and smooth maps, Tangent spaces and differentials , Regular and singular values , Manifolds with boundary, Immersions and embeddings , Degree mod 2 , Orientation of manifolds and Applications of degree.

The first half of the book deals with degree theory, the Pontryagin construction, intersection theory, and Lefschetz numbers. The second half of the book is devoted to differential forms and deRham cohomology.

This note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.

This book presents some basic concepts and results from algebraic topology. Topics covered includes: Smooth manifolds revisited, Stratifolds, Stratifolds with boundary: c-stratifolds, The Mayer-Vietoris sequence and homology groups of spheres, Brouwer�s fixed point theorem, separation and invariance of dimension, Integral homology and the mapping degree, A comparison theorem for homology theories and CW-complexes, Kunneth�s theorem, Singular cohomology and Poincare duality, Induced maps and the cohomology axioms, The Chern classes, Pontrjagin classes and applications to bordism, Constructions of stratifolds.

This book gives a deeper account of basic ideas of differential topology than usual in introductory texts. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail. Topics covered includes: Continuity, compactness and connectedness, Smooth manifolds and maps, Regular values and Sard�s theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler characteristic.