Lecture Notes on Differentiable Manifolds

Lectures on Riemannian Geometry, Part II: Complex Manifolds

This is a set of introductory lecture notes on the geometry of complex manifolds. It is the second part of the course on Riemannian Geometry given at the MRI Masterclass in Mathematics, Utrecht, 2008. The first part was given by Prof. E. van den Ban, and his lectures notes can be found on the web-site of this course, http://www.math.uu.nl/people/ban/riemgeom2008/riemgeom2008.html. Topics that w...

Notes on Differentiable Manifolds

Lectures on complex geometry, Calabi–Yau manifolds and toric geometry

These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...

A Very Long Lecture on the Physical Approach to Donaldson and Seiberg-Witten Invariants of Four-Manifolds

These are lecture notes for a lecture at the Simons Center for Geometry and Physics School on Mathematical Applications of Supersymmetric Yang Mills Theory, March 8, 2012

Varadarajan's book began as a set of lecture notes in a course on Lie groups and is intended to "introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes

bundle are defined using the Chern classes of the complexification of the vector bundle. These are integral characteristic classes in dimensions divisible by 4. With this, all of the characteristic classes to be considered in the book have been defined. The rest of the body of the text is devoted to applications of the characteristic classes. First is an application to partial calculation of th...