Abstract
Abstract
In this paper, using homotopy theoretical methods we study the degrees of maps between
-connected
-dimensional Poincaré complexes. Necessary and sufficient algebraic conditions for the existence of mapping degrees between such Poincaré complexes are established. These conditions allow us, up to homotopy, to construct explicitly all maps with a given degree.
As an application of mapping degrees, we consider maps between
-connected
-dimensional Poincaré complexes with degree
, and give a sufficient condition for these to be homotopy equivalences. This resolves a homotopy theoretical analogue of Novikov’s question: when is a map of degree
between manifolds a homeomorphism? For low
, we classify, up to homotopy, torsion free
-connected
-dimensional Poincaré complexes.
Bibliography: 29 titles.
Subject
Algebra and Number Theory