**M. J. Dupré, J. F. Glazebrook**

##
Relative Inversion and Embeddings

**Abstract:**

Commencing from a monoidal semigroup A, we consider the geometry of the space
W(A) of pseudoregular elements. When A is a Banachable algebra we show that
there exist certain subspaces of W(A) that can be realized as submanifolds of A.
The space W(A) contains certain subspaces constituting the Stiefel manifolds of
framings for A. We establish several embedding results for such subspaces, where
the relevant maps induce embeddings of associated Grassmann manifolds.

**Keywords:**

Banachable algebra, pseudoregular elements, relative inverse, rational retract,
Stiefel manifold.

**MSC 2000:** 46H99, 46M20, 58B25