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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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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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Elliptic Curves and Algebraic Topology 2

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Description: This note covers the following topics: Geometric reformulation, The Adams-Novikov spectral sequence, Elliptic cohomology, What is TMF, Geometric and Physical Aspect.

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

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

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Lectures on Topics in Algebraic K-theory II

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A Concise Course in Algebraic Topology

By: J. P. May

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.

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Lecture Notes in Algebraic Topology I

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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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A Geometric Introduction to K Theory ; Topology

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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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Geometric Topology Localization, Periodicity, and Galois Symmetry I

By: Dennis Sullivan

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 in°uence on the development of both algebraic and geometric topology, pioneering

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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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Algebraic Topology Lecture Notes 3

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K-theory and Geometric Topology

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

By: David Mond

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A Concise Course in Algebraic Topology, J. P. May

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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.

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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...

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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.

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