Description

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I. Preliminaries.- 1.1. Whitney stratifications.- 1.2. Subanalytic sets and semialgebraic sets.- 1.3. PL topology and C? triangulations.- II. X-Sets.- 11.1. X-sets.- 11.2. Triangulations of X-sets.- 11.3. Triangulations of X functions.- 11.4. Triangulations of semialgebraic and X0 sets and functions.- 11.5. Cr X-manifolds.- 11.6. X-triviality of X-maps.- 11.7. X-singularity theory.- III. Hauptvermutung For Polyhedra.- III.1. Certain conditions for two polyhedra to be PL homeomorphic.- III.2. Proofs of Theorems III.1.1 and III.1.2.- IV. Triangulations of X-Maps.- IV.l. Conditions for X-maps to be triangulable.- IV.2. Proofs of Theorems IV.1.1, IV.1.2, IV.1.2? and IV.1.2?.- IV.3. Local and global X-triangulations and uniqueness.- IV.4. Proofs of Theorems IV.1.10, IV.1.13 and IV.1.13?.- V. D-Sets.- V.1. Case where any D-set is locally semilinear.- V.2. Case where there exists a D-set which is not locally semilinear.- List of Notation.