IJPAM: Volume 20, No. 3 (2005)


E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Let $X$ be either a $C^\infty$ paracompact differential manifold or a real analytic manifold. Then for any integer $n\ge 2$ there is a fundamental system of open neighborhoods $\{U_{n,\gamma }\}_{\gamma \in \Gamma _n}$ of the small diagonal $\Delta _{X,n}$ of $X^n$ in $X^n$ such that:

each $U_{n,\gamma }$ is invariant for the action of $S_n$;
for each $n\ge 2$ and each $\gamma \in \Gamma _n$ there is an $S_n$-invariant differentiable submersion (or an $S_n$-invariant real analytic submersion) $u_{n,\gamma }: U_{n,\gamma } \to \Delta _{X,n}$ such that $u_{n,\gamma }\vert \Delta _{X,n} = \mbox{\rm Id}_{\Delta _{X,n}}$.

This is a partially defined solution for the so-called social choice problem introduced by G. Chichilnisky.

Received: March 30, 2005

AMS Subject Classification: 14H99, 32J18, 58A05, 58A07, 90A14, 90A08

Key Words and Phrases: tubular neighborhood, Albanese variety, social choice, market equilibrium

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 3