Introduction to Differential Topology by Uwe Kaiser

Differential Topology by Andrew Kobin

This note covers Smooth manifolds, Regular values, Transversality and embeddings, Vector bundles.

Author(s): Andrew Kobin

52 Pages

Topics in Differential Topology by Mohammad F Tehrani

This note explains the following topics: preliminaries, Different homology theories and their interaction, Classifying spaces, An introduction to symplectic topology.

Author(s): Mohammad F Tehrani

104 Pages

Topology from the Differentiable Viewpoint

This PDF covers the following topics related to Differential Topology : Smooth manifolds and smooth maps, Tangent spaces and derivatives, Regular values, The fundamental theorem of algebra, The theorem of Sard and Brown, Manifolds with boundary, The Brouwer fixed point theorem, Proof of Sard's theorem, The degree modulo 2 of a mapping, Smooth homotopy and smooth isotopy, Oriented manifolds, The Brouwer degree, Vector fields and the Euler number, Framed cobordism, the Pontryagin construction, The Hopf theorem, Exercise.

Author(s): John W. Milnor, Princeton University

77 Pages

Introduction to Differential Topology by Uwe Kaiser

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.

Author(s): Uwe Kaiser

110 Pages