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: Basic Algebra of Polynomials, Induction and the Well ordering Principle, Sets, Some counting principles, The Integers, Unique factorization into primes, Prime Numbers, Sun Ze's Theorem, Good algorithm for exponentiation, Fermat's Little Theorem, Euler's Theorem, Primitive Roots, Exponents, Roots, Vectors and matrices, Motions in two and three dimensions, Permutations and Symmetric Groups, Groups: Lagrange's Theorem, Eul...
Description: Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a eld.
Description: This book explains the following topics: Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some application, Covering spaces and Classification of covering space.
Description: This book covers the following topics: Cell complexes and simplical complexes, fundamental group, covering spaces and fundamental group, categories and functors, homological algebra, singular homology, simplical and cellular homology, applications of homology.
Description: This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including fibrations and cofibrations, Poincare duality for manifolds and manifolds with boundary.
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
Description: This note covers the following topics: Vector Bundles, Classifying Vector Bundles, Bott Periodicity, K Theory, Characteristic Classes, Stiefel-Whitney and Chern Classes, Euler and Pontryagin Classes, The J Homomorphism.
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 book covers the following topics: Cell complexes and simplical complexes, fundamental group, covering spaces and fundamental group, categories and functors, homological algebra, singular homology, simplical and cellular homology, applications of homology.``
Description: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology, Circle bundles.
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 covers the following topics: The Mayer-Vietoris Sequence in Homology, CW Complexes, Cellular Homology,Cohomology ring, Homology with Coefficient, Lefschetz Fixed Point theorem, Cohomology, Axioms for Unreduced Cohomology, Eilenberg-Steenrod axioms, Construction of a Cohomology theory, Proof of the UCT in Cohomology, Properties of Ext(A;G).
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: 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: 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: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology
Description: This book explains the following topics: Some Underlying Geometric Notions, The Fundamental Group, Homology, Cohomology and Homotopy Theory.