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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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Elliptic Curves and Algebraic Topology 2

By: Matthew Ando

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

By: J. P. May; K. Ponto

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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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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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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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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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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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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Lecture Notes on Algebraic K-theory I

By: John Rognes
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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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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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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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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

By: Hopkins Michael; Akhil Mathew

Description: This lecture note explains everything about Algebraic Topology.

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

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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