Gerbes Δεσμών και Συνεστραμμένη Κ-Θεωρία

Postgraduate Thesis uoadl:1321097 406 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2012-10-03
Year:
2012
Author:
Ζαβιτσάνος Γιώργος
Supervisors info:
Ανδρουλιδάκης Ιάκωβος Επικ. Καθηγ.
Original Title:
Gerbes Δεσμών και Συνεστραμμένη Κ-Θεωρία
Languages:
Greek
Summary:
We introduce the notion of bundle grebes and give the basic features of their
theory. As we explicitly show, these are geometric objects that are associated
with degree 3 integral Cech cohomology class on a manifold M, known as
Dixmier-Douady class, in analogy to the 2 integral Cech cohomology class that
is associated to every line bundle through the Chern class isomorphism. We give
the constructions of lifting bundle gerbe as well as the tautological bundle
gerbe and we show that the Dixmier-Douady class induces a bijection between the
classes of stable isomorphic bundle gerbes and the group H^3(M,Z).
We define the K-theory of bundle grebes and we investigate the relation to
twisted K-theory which is defined according to Atiyah’s view, making use of the
classifying space of Fredholm operators. When the Dixmier-Douady class is
torsion, we show that the K-theory of bundle gebres and twisted K-theory
coincide. In the case of non-torsion class, K-theory of bundle gerbes is
defined in analogous way considering the classifying space of zero-index
Fredholm operators.
Keywords:
Bundle gerbes, Τwisted K-theory, Deligne cohomology, Fredholm operators, Dixmier-Douady class
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
31
Number of pages:
72
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