IJPAM: Volume 60, No. 1 (2010)

MICROLINEARITY IN FRÖLICHER SPACES
- BEYOND THE REGNANT PHILOSOPHY OF MANIFOLDS -

Hirokazu Nishimura
Institute of Mathematics
University of Tsukuba
Tsukuba, Ibaraki, 305-8571, JAPAN
e-mail: [email protected]


Abstract.Frölicher spaces and smooth mappings form a Cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-223] that its full subcategory of Weil exponentiable Frölicher spaces is Cartesian closed. By emancipating microlinearity from within a well-adapted model of synthetic differential geometry to Frölicher spaces, we get the notion of microlinearity for Frölicher spaces. It is shown in this paper that its full subcategory of Weil exponentiable and microlinear Frölicher spaces is Cartesian closed. The canonical embedding of Weil exponentiable Frölicher spaces into the Cahiers Topos is shown to preserve microlinearity besides finite products and exponentiation.

Received: December 11, 2009

AMS Subject Classification: 58A03

Key Words and Phrases: microlinearity, synthetic differential geometry, Frölicher space, transversal limit diagram, Topos theory, infinite-dimensional differential geomery, Cahiers Topos, Cartesian closed category, Weil algebra, Weil functor, nilpotent infinitesimal

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1