\(\mathbb{D}^ \infty\)-cohomology groups and \(\mathbb{D}^ \infty\)-maps on submanifolds in Wiener spaces (Q1193911)

In the context of Malliavin calculus the author defines \(D^ \infty\)- maps between two submanifolds in Wiener space. Further, the pullback by the \(D^ \infty\)-map is introduced. It turns out that the pullback has properties analogous to standard properties of the pullback in finite- dimensional case. The retract map is defined and it is proved that the \(D^ \infty\)-cohomology group of a submanifold which is a retract of Wiener space vanishes. A nontrivial example of a submanifold which is a retract of Wiener space is given.