In mathematics, simple homotopy theory is a homotopy theory (a branch of algebraic topology) that concerns with the simple-homotopy type of a space. It was originated by J. H. C. Whitehead in his 1950 paper "Simple homotopy types".
See also Whitehead torsion
References
Cohen, M. M. (1973). A Course in Simple-Homotopy Theory. Graduate Texts in Mathematics. Vol. 10. doi:10.1007/978-1-4684-9372-6. ISBN 978-0-387-90055-1. Hatcher, A. E. (1975). "Higher Simple Homotopy Theory". Annals of Mathematics. 102 (1): 101–137. doi:10.2307/1970977. JSTOR 1970977. Whitehead, J. H. C. (1950). "Simple Homotopy Types". American Journal of Mathematics. 72 (1): 1–57. doi:10.2307/2372133. JSTOR 2372133.
Further reading Simple homotopy theory at the nLab A lecture by J. Lurie.