Switzer Algebraic Topology Homotopy And Homology Pdf May 2026

Homotopy is a fundamental concept in algebraic topology that describes the continuous deformation of one function into another. In essence, homotopy is a way of measuring the similarity between two functions. Two functions are said to be homotopic if one can be continuously deformed into the other without leaving the space.

where ∂_n is the boundary homomorphism. switzer algebraic topology homotopy and homology pdf

H_n(X) = ker(∂ n) / im(∂ {n+1})

where each C_n is an abelian group, and the homomorphisms satisfy certain properties. The homology groups of a space X are defined as the quotient groups: Homotopy is a fundamental concept in algebraic topology