Poincare Immersions.
by John R. Klein
Wayne State University
klein@math.wsu.edu
This paper establishes a Poincare variant of the fundamental theorem of
immersion theory. It has been already accepted for publication
in Forum Mathematicum.
Given a map f:M^n --> X^n with M and X n-dimensoinal
Poincare duality spaces (with or without boundary). One says
that f *immerses* if f x id : M x D^j ---> X x D^j is the underlying
map of a Poincare embedding for sufficiently large j.
Theorem A of this paper says that f immerses if and only if
the pullback of the Spivak normal fibration of X is stable
fiber homotopy equivalent to the Spivak normal fibration of M.
Also included is a new homotopy theoretic
proof (using equivariant duality) of the existence
and uniqueness theorems for the Spivak fibration.