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.
Introduction to Differential Topology by Uwe KaiserUwe KaiserPDF
| 110 Pages
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
Differential Algebraic TopologyMatthias KreckPDF
| 168 Pages
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 DundasBjorn Ian DundasPDF
| 210 Pages
This note covers the following
topics: Smooth manifolds, The tangent space, Regular values, Vector bundles,
Constructions on vector bundles and Integrability.
Introduction To Differential TopologyJoel W. Robbin and Dietmar A. SalamonPDF
| 207 Pages
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)Sergei TabachnikovPDF
| 20 Pages
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.