On tangent cones of Frölicher spaces

Abstract

Tangent spaces, tangent cones, invertible pairs, and various other notions common to differential geometry are defined for Frölicher spaces in a natural way and seen to coincide with their counterparts for smooth finite dimensional manifolds. The geometry of the wedge product space R∨R, where R is the canonical one-dimensional Euclidean Frölicher space, is studied in great detail. Invertible pairs, as shown in the paper, are very indispensable tools when understanding the geometry of a Fröolicher space locally. Unfortunately the inverse function theorem for smooth manifolds does not exist in the context of Fröolicher spaces.