Thom's conjecture on triangulations of maps (Q1818712)

Two proper maps, \(f_i: X_i\to Y_i\) between closed subsets of \(E^n\) are R-L equivalent if there exist maps \(\eta:Y_1\to Y_2\), \(\tau: X_1\to X_2\) so that \(\eta\circ f_1=f_2\circ\tau\). A map is called triangulable if it is R-L equivalent to a PL map. In [Enseign. Math., II. Sér. 8, 24-33 (1962; Zbl 0109.40002)] \textit{R. Thom} conjectured that a map ``stratifiée sans éclatement'' is triangulable. The author proves a more general form of this conjecture.