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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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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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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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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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Algebraic Topology Hatcher

By: Allen Hatcher

Description: This book explains the following topics: Some Underlying Geometric Notions, The Fundamental Group, Homology, Cohomology and Homotopy Theory.

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Algebraic Topology Lecture Notes 1

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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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 Hatcher

By: Allen Hatcher

Description: This book explains the following topics: Some Underlying Geometric Notions, The Fundamental Group, Homology, Cohomology and Homotopy Theory.

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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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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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Differential Topology Lecture Notes 2

By: Wolf Michael M.

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...

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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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Algebraic Topology Class Notes 1

By: Sjerve Denis; Benjamin Young

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).

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

By: J. P. May; K. Ponto
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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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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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Algebraic L Theory and Topological Manifolds

By: A. A. Ranicki
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Metric and Topological Spaces

By: T. W. Korner

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.

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An Introduction to K-theory ; Topology

By: Eric M. Friedlander

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.

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Lecture Notes on Algebraic K-theory I

By: John Rognes
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