Description: This lecture note explains everything about Algebraic Topology.
Description: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology, Circle bundles.
Description: This note covers the following topics: Background Linear Algebra, Lie Algebras: Definition and Basic Properties, Solvable Lie Algebras and Lie s Theorem, Nilpotent Lie Algebras and Engel s Theorem, Cartan s Criteria for Solvability and Semisimplicity, Semisimple Lie Algebras, root Space Decompositions, Classical Simple Complex Lie Algebras.
Description: This note covers the following topics: Chain Complexes, Homology, and Cohomology, Homological algebra, Products, Fiber Bundles, Homology with Local Coefficient, Fibrations, Cofibrations and Homotopy Groups, Obstruction Theory and Eilenberg-MacLane Spaces, Bordism, Spectra, and Generalized Homology and Spectral Sequences.
Description: Lectures given at the School on Algebraic K-theory and its Applications
Description: This note provides an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible to participants with little or no prior knowledge of the subject.
Description: This book explains the following topics: Some Underlying Geometric Notions, The Fundamental Group, Homology, Cohomology and Homotopy Theory.
Description: This book explains the following topics: The fundamental group and some of its applications, Categorical language and the van Kampen theorem, Covering spaces, Graphs, Compactly generated spaces, Cofibrations, Fibrations, Based cofiber and fiber sequences, Higher homotopy groups, CW complexes, The homotopy excision and suspension theorems, Axiomatic and cellular homology theorems, Hurewicz and uniqueness theorems, Singular homology theory, An introduction to K theory.
Description: This note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.
Description: First part of this course note presents a rapid overview of metric spaces to set the scene for the main topic of topological spaces.Further it covers metric spaces, Continuity and open sets for metric spaces, Closed sets for metric spaces, Topological spaces, Interior and closure, More on topological structures, Hausdorff spaces and Compactness.
Description: There are two reasons why this may be a useful exercise. First, it may help to show K-theorists brought up in the \algebraic school how their subject is related to topology. And secondly, clarifying the relationship between K- theory and topology may help topologists to extract from the wide body of K-theoretic literature the things they need to know to solve geometric problems
Description: This is one day going to be a textbook on K-theory, with a particular emphasis on connections with geometric phenomena like intersection multiplicities.
Description: This note covers the following topics: The Fundamental Group, Covering Projections, Running Around in Circles, The Homology Axioms, Immediate Consequences of the Homology Axioms, Reduced Homology Groups, Degrees of Spherical Maps again, Constructing Singular Homology Theory.
Description: Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a eld.
Description: We will follow a direct approach to differential topology and to many of its applications without requiring and exploiting the abstract machinery of algebraic topology. The course will cover immersion, submersions and embeddings of manifolds in Euclidean space (including the basic results by Sard and Whitney), a discussion of the Euler number and winding numbers, fixed point theorems, the Borsuk-Ulam theorem and respective applications. At the end of the cou...
Description: The seminal `MIT notes' of Dennis Sullivan were issued in June 970 and were widely circulated at the time. The notes had a ma- or inÂ°uence on the development of both algebraic and geometric topology, pioneering