Description: Lectures given at the School on Algebraic K-theory and its Applications
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 lecture note explains everything about Algebraic Topology.
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: 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: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology
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: 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 note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.
Description: This note explains the following topics: Cohomology, The Mayer Vietoris Sequence, Compactly Supported Cohomology and Poincare Duality, The Kunneth Formula for deRham Cohomology, Leray-Hirsch Theorem, Morse Theory, The complex projective space.
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: 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: 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 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: The first half of the book deals with degree theory, the Pontryagin construction, intersection theory, and Lefschetz numbers. The second half of the book is devoted to differential forms and deRham cohomology.
Description: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology, Circle bundles.