LOCAL INVERSION OF A CLASS OF PIECEWISE REGULAR MAPS

This paper provides sufficient conditions for any map L, that is strongly piecewise linear relatively to a decomposition of R-k in admissible cones, to be invertible. Namely, via a degree theory argument, we show that when there are at most four convex pieces (or three pieces with at most a non convex one), the map is invertible. Examples show that the result cannot be plainly extended to a greater number of pieces. Our result is obtained by studying the structure of strongly piecewise linear maps. We then extend the results to the PC1 case.