Deformation retraction

cjerdonek authored on Nov. 3, 2020, 11:51 a.m.

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	In mathematics (and specifically topology), a deformation retraction captures the idea of deforming a space over time into a subspace of itself. Specifically, given a topological space \(X\) and a subspace \(A\) of \(X\), a deformation retraction is a homotopy from the identity map on \(X\) to a map from \(X\) to \(A\) that is the identity on \(A\). In addition, if the homotopy is the identity on \(A\) for all maps in the family (i.e. not just the first and final maps), then the deformation retraction is said to be a strong deformation retraction.

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In mathematics (and specifically topology), a deformation retraction captures the idea of deforming a space over time into a subspace of itself.

Specifically, given a topological space \(X\) and a subspace \(A\) of \(X\), a deformation retraction is a homotopy from the identity map on \(X\) to a map from \(X\) to \(A\) that is the identity on \(A\). In addition, if the homotopy is the identity on \(A\) for all maps in the family (i.e. not just the first and final maps), then the deformation retraction is said to be a strong deformation retraction.

cjerdonek / Deformation retraction 53a9113200597fdc97b004101451e7446f63799d