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Algebraic Topology Lecture Note

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Description

Name of Notes : – Algebraic Topology Lecture Note

Introduction

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.

Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.

Modules / Lectures

  • Module 1: General Introduction
  • Module 2: General Topology
  • Module 3: Fundamental groups and its basic properties
  • Module 4:Theory Covering Spaces
  • Module 5:Seifert Van kampen Theorem & its application
  • Module 6 :Basic Homology Theory
  • Module 7:Relative homology,exicism and the Jordan Brouwer separation therom