REIDEMEISTER TORSION AND SEIBERG-WITTEN THEORY (1997)
4PM on Tuesdays, Room 5325, starting October 7.
Reidemeister torsion was invented in the 1930's as a tool for studying
the topology of 3-dimensional manifolds, such as lens spaces. In the 1950's
and 1960's it was incorporated into the theory of Whitehead torsion, and
was applied to high-dimensional manifold theory. In the last two years
it has returned in the study of low-dimensional manifolds, via a possible
connection with the 3-dimensional analogue of the original 4-dimensional
Seiberg-Witten invariants.
We plan a reading seminar to learn about Reidemeister torsion and its
applications, with a view to understanding some of the following papers:
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1. Milnor, "Infinite cyclic covers" (Collected Works, Vol. II)
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2. Turaev, "Reidemeister torsion in knot theory" (Russian Math. Surveys
41 (1986), 119-182)
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3. Hutchings and Lee, "Circle valued Morse theory,
Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds"(preprint)
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4. Turaev, "Torsion invariants of Spin^c-structures on 3-manifolds", (preprint)
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5. Hutchings and Lee, "Circle valued Morse theory
and Reidemeister torsion" (preprint)
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6. Meng and Taubes, "SW = Milnor torsion", Math. Res. Lett 3 (1996), 661-674
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7. Pazhitnov, "Simple homotopy type of Novikov complex
for closed 1-forms and Lefschetz zeta-functions of the gradient flow"
(preprint)
TIMETABLE
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Tuesday, 7th October, 4PM (Room 5325), Andrew Ranicki
Reidemeister torsion -- Milnor, Turaev
Notes on Reidemeister torsion --
PDF format --
DVI format --
PS format
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Tuesday, 14th October, 4PM (Room 5325), Justin Roberts
Spin structures -- Turaev I
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Tuesday, 21st October, 4PM (Room 5325), Justin Roberts
Spin structures -- Turaev II
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Tuesday, 4th November, 4PM (Room 5325), Alexei Kovalev
Seiberg-Witten theory -- Meng-Taubes I
Notes on Seiberg-Witten theory --
PDF format --
DVI format --
PS format
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Thursday, 13th November, 4PM (Room 4312), Alexei Kovalev
Seiberg-Witten -- Meng-Taubes II
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Tuesday, 18th November, 4PM (Room 5325), Elmer Rees
Morse theory -- Hutchings-Lee, Pazhitnov I
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Tuesday, 2nd December, 4PM (Room 5325), Elmer Rees
Morse theory -- Hutchings-Lee, Pazhitnov II
(There will be no meeting in the week November 24-29. Victor Buchstaber
will talk at 4PM on Tuesday, 25th November in Room 5325 on "Toric manifolds
and complex cobordism").