Algebraic Toplogy: A guide to literature

• objectives
• precautions

Table of Contents

Basics

• how to search literature
• homology and cohomology
• homotopy groups and homotopy sets
• important spaces and operations on them
• maps
• history of topology

Important Tools and Concepts

• categories and functors
• spectral sequences
• algebraic tools
• cohomology operations
• K -theory
• cobordisms and related topics
• simplicial and cosimplicial techniques
• homotopical algebra
• stable homotopy theory
• sheaves and related concepts
• operads and related concepts

Connections to Other Subjects

• geometry and topology of manifolds and other geometric objects
• configurations
• combinatorics
• algebraic geometry
• number theory and related topics
• vertex algebras and related fields
• physics
• analysis
• topology and computer
• economics
• biology
• engineering
• statistics

Selected Topics

• categorical structures
• topology of mapping spaces
• topological groups and Lie groups
• homotopy algebras
• chromatic phenomena in stable homotopy theory
• chromatic phenomena in unstable homotopy theory
• calculus of functors
• homotopy theory of stratified spaces
• elliptic cohomology and related topics
• equivariant topology
• Lusternik-Schnirelmann category and related topics

Preliminaries

• calculus
• linear algebra
• set theory and logic
• point set topology
• group theory
• basics of algebra
• classical geometry