As the seminar progresses, we will build a bibliography of
all books, papers, web pages, and other references that
we use. When available, the references include a link to a
free PDF.
The main stated goal of the seminar is to study the following paper:
Main Reference:
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[NS]
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J. Navarro and J.B. Sancho, Peetre-Slovák's theorem revisited. Preprint, 2016.
arXiv: 1411.7499
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To ensure that this paper is accessible to a larger audience, we will begin the seminar by
"reviewing" key ideas from differential topology,
differential geometry, abstract algebra, algebraic topology, and category theory. My lectures
will primarily follow [PP], using the other references to expound on a topic when necessary. I
will update this list periodically throughout the semester.
Differential Topology:
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[GP]
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V. Guillemin and A. Pollack, Differential Topology, Providence:
AMS Chelsea, 1974.
|
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[H]
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M. Hirsh, Differential Topology, GTM 33. New York:
Springer, 1976.
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[L]
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J. Lee, Introduction to Smooth Manifolds, GTM 218.
New York: Springer, 2003.
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[PP]
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P.E. Parker, Lectures on Differential Manifolds,
Bundles, and Groups.
DGS
Preprint P11-PBR1, Wichita: 2015.
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Differential Geometry:
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[O]
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B. O'Neill, Semi-Riemannian Geometry.
New York: Academic Press, 1983.
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[P]
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W. Poor, Differential Geometric Structures.
New York: McGraw-Hill, 1981. (Dover reprint, 2007.)
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[KMS]
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I. Kolář, P. Michor, and J. Slovák, Natural Operators in
Differential Geometry.
URL --
https://www.mat.univie.ac.at/~michor/kmsbookh.pdf
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Differential Operators:
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[AA]
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A. Avantaggiati (ed.), Pseudodifferential Operators with Applications, CIME
Summer Schools 75, Napoli:
Springer, 1978. (Reprint: Berlin, 2010)
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[S]
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J. Slovák, Peetre Theorem for Nonlinear Operators, Ann. Global Anal.
Geom. 6 (1988) 273-283.
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