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This section contains free e-books and guides on Differential Topology, some of the resources in this section can be viewed online and some of them can be downloaded.

Differential Topology Books
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Introduction to Differential Topology by Uwe Kaiser

PDF | 110 Pages | English
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 Sardís theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler characteristic.

 
Differential Algebraic Topology

PDF | 168 Pages | English
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, Brouwerís fixed point theorem, separation and invariance of dimension, Integral homology and the mapping degree, A comparison theorem for homology theories and CW-complexes, Kunnethís theorem, Singular cohomology and Poincare duality, Induced maps and the cohomology axioms, The Chern classes, Pontrjagin classes and applications to bordism, Constructions of stratifolds.

 
Differential Topology by Bjorn Ian Dundas

PDF | 210 Pages | English
This note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.

 
Introduction To Differential Topology

PDF | 207 Pages | English
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.

 
Differential topology Lecture notes (PDF 20p)

PDF | 20 Pages | English
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.

 
Combinatorial Differential Topology and Geometry (PDF 30p)

PDF | 30 Pages | English
This note explains how two standard techniques from the study of smooth manifolds, Morse theory and Bochnerís method, can be adapted to aid in the investigation of combinatorial spaces.

 
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