A Course in Simple Homotopy Theory

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... that, when K has only finitely many cells, CW and CW are auto matically satisfied A map cp:Q" ->- K, as in CW 2, is called a characteristic map Clearly such a map 'I' gives rise to a characteristic... subcomplex of K and K = L u aA where a is a vertex of K, A and aA are simplexes of K, and aA n L = aA Schematically, We say that K col/apses simplicial/y to L written K '! L-if there is a finite sequence... 31 Matrices and formal deformations matrix i s the identity The following lemma shows that certain algebraic changes of the matrix of a given pair can be realized by expanding and collapsing

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