On the additivity property of the generalized degree.

Abstract

The classical theory of the degree of a map f: Sn !Sn has been extended by many authors. K. G ‘ eba, I. Massab`o and A. Vignoli [in Nonlinear functional analysis and its applications (Maratea,1985), 55–73, Reidel, Dordrecht, 1986; have defined a degree for f:U !Rn, where U Rn+k is a bounded open subset on whose boundary f does not vanish. The goals of the present paper consist of (i) an alternative description using the language of framed cobordism, and (ii) an example to show that this generalized degree is not additive—in general—with respect to disjoint open sets U.