Tsuyoshi KOBAYASHI Home Page

2008 Nara Topology Seminar

12ŒŽ16“úi‰ÎjŒßŒã‚SF‚Q‚O`‚T:‚T‚O

êŠF“ޗǏ—Žq‘åŠw—Šw•”‚b“‚SŠK‚S‚R‚Pi‰‰KŽºj

u‰‰ŽÒFProf. Andrei Pajitnov (Universite de Nantes)

u‰‰‘è–ځF On the Morse-Novikov number and the tunnel number of knots

Abstract:
Let K be a knot in the three-sphere. The Morse-Novikov number
MN(K) of K is the minimal number of critical points of a regular
circle-valued Morse function defined on the complement of K.
We prove that MN(K) is less than or equal to twice the tunnel
number of the knot and present consequences of this result.

6ŒŽ10“úi‰ÎjŒßŒã‚SF‚Q‚O`‚T:‚T‚O

êŠF“ޗǏ—Žq‘åŠw—Šw•”‚b“‚SŠK‚S‚R‚Pi‰‰KŽºj

u‰‰ŽÒFProf. Ken Shackletoni“Œ‹žH‹Æ‘åŠwj

u‰‰‘è–ځF Computing distances in two pants complexes

Abstract: The pants complex is an accurate combinatorial
model for the Weil-Petersson metric (WP) on Teichmueller space
(Brock). One hopes that many of the geometric properties
of WP are accurately replicated in the pants complex, and
this is the source of many open questions. We compare these
in general, and then focus on the 5-holed sphere and the
2-holed torus, the first non-trivial surfaces. We arrive at
n algorithm for computing distances in the (1-skeleton of the)
pants complex of either surface.

5ŒŽ7“úi‹àj14:40-16:40

êŠF“ޗǏ—Žq‘åŠw—Šw•”C“4ŠK@434i¬u‹`Žºj

u‰‰ŽÒFProf. Joseph Maher iOklahoma State Universityj

u‰‰‘è–ځFHeegaard splittings and virtual fibers

Abstract: We show that if a manifold has infintely many covers of bounded
Heegaard genus, then the manifold is virtually fibered. This
generalizes a result of Lackenby.

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1ŒŽ25“úi‹àj14:40-16:10

êŠF“ޗǏ—Žq‘åŠw—Šw•”VB“‚SŠK@B1406i”ŠwŠK’i‹³Žºj

u‰‰ŽÒFProf. Mattman, Thomas (California State University)

u‰‰‘è–ځF(Student Talk) A brief overview of Culler-Shalen Theory

Abstract: We give an overview of the Culler-Shalen seminorm and its
use in analysing cyclic and finite surgery of hyperbolic knots. In
particular, we will focus on the case of small hyperbolic knots in
S^3. This talk will serve as an introduction to a second talk on
cyclic and finite surgeries on pretzel knots.

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1ŒŽ25“úi‹àj16:20-17:50

êŠF“ޗǏ—Žq‘åŠw—Šw•”VB“‚SŠK@B1406i”ŠwŠK’i‹³Žºj

u‰‰ŽÒFProf. Mattman, Thomas (California State University)

u‰‰‘è–ځFCyclic and Finite Surgeries on Pretzel Knots

Abstract: We classify cyclic surgeries on pretzel knots; there are
no non-trivial cyclic surgeries other than those along slope 18 and
19 of the (-2,3,7) pretzel knot. For finite surgeries, we provide
evidence that only the (-2,3,7) and (-2,3,9) knots admit non-
trivial finite surgeries. In particular, we show that this is true
except, possibly, for pretzel knots of the form (-2,p,q) with p
\geq q \geq 5.