Topology

Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. When the discipline was first introduced it was called analysis situs (Latin analysis of place).

Outline of the deeper theory

• (Co)fibre sequences: Puppe sequence, computations
• Homotopy groups of spheres
• Obstruction theory
• K-theory: KO-theory, algebraic K-theory
• Stable homotopy theory
• Brown's representability theorem
• (Co)bordism
• Signatures
• Brown-Peterson BP and Morava K-theory
• Surgery obstructions
• H-spaces, infinite loop spaces, A_∞ rings
• Homotopy theory of affine schemes
• Intersection cohomology