EXTENSIONS OF HOMEOMORPHISMS BETWEEN LIMBS OF THE MANDELBROT SET Bodil Branner and Nuria Fagella* *Departament de Matematica aplicada i Analisi Universitat de Barcelona Gran Via 585 08005 Barcelona Spain e-mail: fagella@maia.ub.es ABSTRACT: Using holomorphic surgery techniques, we construct a homeomorphism between a neighborhood of any limb of the Mandelbrot set and a neighborhood of any other of equal denominator, in such a way that the limbs are mapped among each other. On the limbs, the homeomorphism coincides with that constructed in [BF], which proves that these maps are compatible with the embedding of the limbs in the plane. [BF] B.~Branner \& N.~Fagella, Homeomorphisms between Limbs of the Mandelbrot Set, {\em J.~Geom.~Anal.} {\bf 9} (1999), 327-390.