IJPAM: Volume 64, No. 1 (2010)

DIFFERENTIAL GEOMETRY OF
MICROLINEAR FRÖLICHER SPACES II

Hirokazu Nishimura
Institute of Mathematics
University of Tsukuba
Tsukuba, Ibaraki, 305-8571, JAPAN


Abstract.In this paper, as the second in our series of papers on differential geometry of microlinear Frölicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as $\mathrm{div}$ (ergence) and $\mathrm{rot}$ (ation) are uniquely determined geometrically or physically in classical vector calculus. This infinitesimal characterization of exterior differentiation has been completely missing in orthodox differential geometry.

Editorial Remark. Please, see International Journal of Pure and Applied Mathematics, 65, No. 1 (2010), here.

Received: June 30, 2010

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: 64
Issue: 1