Fan Blowup of Analytic Surgery Spaces

Date of Award

2011

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Global Anyalysis, Analytic Surgery, Manifolds with Corners

Area of Concentration

Mathematics

Abstract

Problems in global analysis often involve pseudodifferential operators which degenerate along submanifolds. The Schwartz kernels of such operators have singularities which arise from two sources: singularities which occur along the diagonal of the product space, and those which arise due to boundary degeneracies. To decouple these sources of singularities, iterated blowup of submanifolds is introduced. Blowup, however is not in general commutative; that is, blowing up a set of submanifolds in different orders does not necessarily give diffeomorphic spaces. This thesis provides a review of the differential geometry of manifolds with corners, as well as a method for determining commutativity of blowups using fan complexes. We give conditions which allow us to use the fan blowup method on submanifolds that are not necessarily boundary faces of a manifold with corners. Finally, we compute specific examples, determining fan complexes for the single and double stretched analytic surgery spaces and proving the commutativity of their blowups.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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