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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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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 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 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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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 L Theory and Topological Manifolds

By: A. A. Ranicki
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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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More Concise Algebraic Topology Localization, Completion, and Mode...

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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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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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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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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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Lectures on Topics in Algebraic K-theory II

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

By: J. P. May

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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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Lectures on K-theory I

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A Concise Course in Algebraic Topology

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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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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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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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