Topology of Stratified Spaces
by Greg Friedman, et al.
Publisher: Cambridge University Press 2011
Number of pages: 477
This book concerns the study of singular spaces using techniques from a variety of areas of geometry and topology and interactions among them. It contains more than a dozen expository papers on topics ranging from intersection homology, L2 cohomology and differential operators, to the topology of algebraic varieties, signatures and characteristic classes, mixed Hodge theory, and elliptic genera of singular complex and real agebraic varieties.
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by Jacob Lurie - Princeton University Press
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
by G. de Rham - Tata Institute of Fundamental Research
These notes were intended as a first introduction to algebraic Topology. Contents: Definition and general properties of the fundamental group; Free products of groups and their quotients; On calculation of fundamental groups; and more.
by Daniel Dugger - University of Oregon
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.
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 ...