Open manifold
In mathematics , an open manifold is a manifold without a boundary , the connected components of which are all non- compact . The opposite concept of an open manifold is that of the closed manifold .
Examples of open manifolds
- the Euclidean space
- any open subset of the
- the dotted torus
- the Whitehead manifold
Tame ends
An end of an open manifold is tame, if a series finally dominated environments with
- and
owns. An open manifold is the interior of a compact, framed manifold if the ends are tame and the seven-man obstruction for all ends
vanishes in the projective limit of the reduced algebraic K-theory of group rings , so .
literature
A. Ranicki , B. Hughes : Ends of complexes , Cambridge Tracts in Mathematics 123, Cambridge University Press (1996).