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 Greg Friedman - arXiv.org
This is an introduction to simplicial sets and simplicial homotopy theory with a focus on the combinatorial aspects of the theory and their geometric/topological origins. Accessible to students familiar with the fundamentals of algebraic topology.
by Peter Saveliev - Intelligent Perception
Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It is called cohomology.
by Boris Dubrovin - arXiv
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.
by J. P. May - Springer
A paper devoted to the study of iterated loop spaces. Our goal is to develop a simple and coherent theory which encompasses most of the known results about such spaces. We begin with some history and a description of the desiderata of such a theory.