A Primer on Homotopy Colimits
by Daniel Dugger
Publisher: University of Oregon 2008
Number of pages: 72
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.
Home page url
Download or read it online for free here:
by Liviu I. Nicolaescu - University of Notre Dame
The author discusses several exciting topological developments which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
by Robin Hartshorne - Springer
The main purpose of these notes is to prove a duality theorem for cohomology of quasi-coherent sheaves, with respect to a proper morphism of locally noetherian preschemes. Various such theorems are already known. Typical is the duality theorem ...
by U. Bruzzo
Introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for algebraically integrable systems and the geometry of quantum field and string theory.
by Jean-Pierre Schneiders - Universidade de Lisboa
This text deals with characteristic classes of real and complex vector bundles and Hirzebruch-Riemann-Roch formula. We will present a few basic but fundamental facts which should help the reader to gain a good idea of the mathematics involved.