Generalized complementing maps

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Google Scholar
Research Projects
Organizational Units
Journal Issue
In this paper we apply the generalized degree introduced by Geba, Massabo and Vignoli, in [3], to extend the notion of complementing maps defined by Fitzpatrick, Massabo and Pejsachowicz, in [1] and [2]. On the other hand, we obtain, in low dimension, a bifurcation result in terms of the linking number of some 1-dimensional manifolds. We also present a global theorem that improves a Rabinowitz’s type result contained in [3] concerning the generalized degree.
P.M. Fitzpatrick, I. Massabo, J. Pejsachowicz: On the overing dimension of the set of solutions of some nonlinear equations. Transactions AMS 296 (1986), no.2, 777–798. P.M. Fitzpatrick, I. Massabo, J. Pejsachowicz: Global several-parameter bifurcation and continuation theorems: a unified approach via complementing maps. Math. Ann. 263 (1983), 61–73. K. Geba, I. Massabo, A. Vignoli: Generalized degree and bifurcation. Nonlinear Funct.Analysis and Appl. (1986), 55–73. K. Geba: Cohomotopy groups and bifurcation. Topological methods in bifurcation theory.Les Presses de l’Universit´e de Montreal, 1985. M.W. Hirsch: Differential topology. Springer-Verlag, Berlin 1976. S.T. Hu: Homotopy theory. Academic Press, 1959. J. Ize, I. Massabo, A. Vignoli: Degree theory for equivariant maps. Transactions AMS 315 (1989),433–510. J. Ize, I. Massabo, J. Pejsachowicz, A.Vignoli: Structure and dimension of global branches of solutions of multiparameter nonlinear equations.Transactions AMS 291(1985), no.2,383–435. M.A. Kervaire: An interpretation of G. Whitehead’s generalization of Hopf’s invariant.Annals of Math. 69 (1959), no.2, 345–365. L.S. Pontryagin: Smooth manifolds and their applications in homotopy theory. Amer.Math. Soc. Translations. 11 (1959), 1–114. F.R. Ruiz del Portal: On the additivity property of the generalized degree. Math. Japonica 37 (1992), 657–664. F.R. Ruiz del Portal: On a generalized degree theory for continuous maps between manifolds.Tsukuba J. Math., 17 (1993), no. 2, 323–338. F.R. Ruiz del Portal: Generalized degree in normed spaces. Publi.Matematiques, Univ. Aut. de Barcelona 36 (1992), 157–166. F.R. Ruiz del Portal: Teorıa del grado topologico generalizado y aplicaciones. Tesis Doctoral, Univ.Complutense de Madrid, 1990.