Harmonic forms under metric and topological perturbations

We construct examples illustrating various aspects of Hodge theory on Riemannian manifolds. We consider the relationship between the harmonic forms on a product space and the harmonic forms on the factors as well as the harmonic forms on a connected sum and the harmonic forms on the summands. Algebraic topology provides relations between the cohomology groups of these spaces via the Kunneth formula and the connected sum formula. We consider the problem of describing these relationships in terms of DeRham cohomology and in terms of Hodge theory. For a connected sum, we use a localization method to produce DeRham representatives on the connected sum from DeRham representatives on the summands. We give an example of a Riemannian connected sum, the double torus, where it is impossible to extend a harmonic form on one summand to the entire connected sum.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kerofsky, Louis Joseph

Contributors dc:contributor

• Tondeur, Philippe

• Mathematics

Statement dc:rights

• Copyright 1995 Kerofsky, Louis Joseph

Language dc:language

eng

Identifier

AAI9624385
(UMI)AAI9624385

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/22489