Existence of in-channels for the plane fixed point problem
by
Lex G. Oversteegen
UAB
Coauthors: Mayer and Tymchatyn

Report on joint work with Bell, Fokkink, Mayer and Tymchatyn

The authors have shown that any composition of open and monotone mappings of the plane is either positively or negatively oriented. They also have shown that positively oriented maps have a fixed point in every invariant acyclic subcontinuum. The case for negatively oriented maps is more difficult. As a first step we outline a proof of the following:

Theorem Suppose that X is a minimal tree-like plane continuum which is invariant under an open, proper and light map of the plane which has no fixed point in X. Then X has a generalized in-channel.

Date received: February 28, 2003