Dissertation committee:
Ιωάννης Εμμανουήλ Αναπλ. Καθηγητής Επιβλέπων, Μιχάλης Μαλιάκας Καθηγητής, Παναγιώτης Παπάζογλου Καθηγητής
Summary:
In this thesis we study a class of maps between CW complexes called phantom
maps. We examine, in particular, a numerical invariant of phantom maps called
the Gray index. A central result describes a new characterization of the Gray
index in terms of the rationalization of a space. Using this characterization,
we develop a method of locating phantom maps of a specific Gray index, by
checking algebraic invariants of the spaces. We use this method in order to
present an example of two spaces, such that there are phantom maps of any Gray
index between them. We also examine the set of phantom maps having infinite
Gray index, using towers of abelian groups. Our proofs use elements of
homology, cohomology and homotopy theory of CW complexes (such as higher
homotopy groups, fibration and cofibration sequences, localization and
completion). We also use extensively methods and tools of homological algebra,
such as the derived functor of the inverse limit.
Keywords:
Homotopy theory, Phantom map, Gray index, Rationalization, lim1
