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Fan Blowup of Analytic Surgery Spaces

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Material Information

Title:
Fan Blowup of Analytic Surgery Spaces
Physical Description:
Book
Language:
English
Creator:
Stanwyck, Brian
Publisher:
New College of Florida
Place of Publication:
Sarasota, Fla.
Creation Date:
2011
Publication Date:

Thesis/Dissertation Information

Degree:
Bachelor's ( B.A.)
Degree Grantor:
New College of Florida
Degree Divisions:
Natural Sciences
Area of Concentration:
Mathematics
Faculty Sponsor:
McDonald, Patrick

Subjects

Subjects / Keywords:
Global Anyalysis
Analytic Surgery
Manifolds with Corners
Genre:
Electronic Thesis or Dissertation
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )

Notes

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.
Thesis:
Thesis (B.A.) -- New College of Florida, 2011
Electronic Access:
RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography:
Includes bibliographical references.
Source of Description:
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.
Local:
Faculty Sponsor: McDonald, Patrick
Statement of Responsibility:
by Brian Stanwyck

Record Information

Source Institution:
New College of Florida
Holding Location:
New College of Florida
Rights Management:
Applicable rights reserved.
Classification:
local - S.T. 2011 S79
System ID:
NCFE004456:00001

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