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Lectures on K-theory I

By: Max Karoubi

Description: Lectures given at the School on Algebraic K-theory and its Applications

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Lecture Notes in Algebraic Topology I

By: Anant R. Shastri

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.``

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Algebraic Topology

By: Hopkins Michael; Akhil Mathew

Description: This lecture note explains everything about Algebraic Topology.

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Lectures on Topics in Algebraic K-theory II

By: Hyman Bass
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International School for Advanced Studies 1

By: U. Bruzzo

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...

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Lie Algebras by Fulton B. Gonzalez

By: Fulton B. Gonzalez

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.

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Algebraic Topology Lecture Note

By: Jarah Evslin; Alexander Wijns

Description: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology

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Vector Bundles K Theory

By: Allen Hatcher

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.

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Introduction to Topology

By: Alex Kuronya

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.

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Differential Topology by Bjorn Ian Dundas

By: Bjorn Ian Dundas

Description: This note covers the following topics: Smooth manifolds, The tangent space, Regular values, Vector bundles, Constructions on vector bundles and Integrability.

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Cohomology,connections, Curvature and Characteristic Classes ; Top...

By: David Mond

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.

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Lecture Notes in Algebraic Topology II

By: James F. Davis; Kirk Paul

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.

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Algebraic Topology Lecture Notes 2

By: David Gauld

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.

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K-theory and Geometric Topology

By: Jonathan Rosenberg

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

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A Geometric Introduction to K Theory ; Topology

By: Daniel Dugger

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.

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Lecture Notes in Algebraic Topology Anant R Shastri

By: Anant R. Shastri

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.

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Introduction to Differential Topology, Part 2

By: Robbin Joel W. ; Dietmar A. Salamon

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.

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Algebraic Topology Lecture Notes 3

By: Evslin Jarah; Alexander Wijns

Description: This note covers the following topics: Group theory, The fundamental group, Simplicial complexes and homology, Cohomology, Circle bundles.

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More Concise Algebraic Topology Localization, Completion, and Mode...

By: J. P. May; K. Ponto
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Lecture Notes on Algebraic K-theory I

By: John Rognes
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