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
note explains the following topics: preliminaries, Different homology theories and their
interaction, Classifying spaces, An introduction to symplectic topology.
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 Sards theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler
characteristic.
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.