In mathematics, simple homotopy theory is a
homotopy theory
In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...
(a branch of
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
) that concerns with the
simple-homotopy type of a space. It was originated by Whitehead in his 1950 paper "Simple homotopy type".
See also
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Whitehead torsion In geometric topology, a field within mathematics, the obstruction to a homotopy equivalence f\colon X \to Y of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion \tau(f) which is an element in the Whitehead group \ope ...
References
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Further reading
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A lecture by J. Lurie
Homotopy theory
Equivalence (mathematics)
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