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University of Michigan
Department of Mathematics
Fall 2004 Topology Seminar
Fridays 4-5, 3096 East Hall
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For more information, contact Bernardo
Uribe.
If you want to check the list of seminars held in previous terms,
click on the appropriate link below.
Winter 2004, Fall 2003, Winter 2003, Fall 2002, the year 2000-1.
Schedule of Talks
Abstracts
September
10
We demonstrate the existence of closed hyperbolic 3-manifolds
which contain no taut R-covered foliation but which have left-orderable
fundamental group. This is joint work with Sergio Fenley.
September
24
We show that every limit group acts properly discontinuously and
cocompactly by isometries on a CAT(0) space. The approach is to notice
that a certain class of limit groups, \omega-residually free towers (for
the suspense sake I won't say what this is until the talk), is
obviously CAT(0). It was shown that every limit group L embeds into some
such thing. One then shows that the L-covering space contains a compact
core which is locally CAT(0). If we are lucky, we might even prove that
these CAT(0) spaces have isolated flats property.
October 1
Let $S$ be a compact, connected, orientable surface of positive
genus. Let $HT(S)$ be the Hatcher-Thurston complex of $S$. We prove that
$Aut(HT(S))$ is isomorphic to the extended mapping class group of $S$
modulo its center. This is a joint work with M.Korkmaz.
October
8
We classify the homotopy type of the space of T^n equivariant symplectic
embeddings from the standard 2n-dimensional ball of some fixed
radius into a 2n-dimensional symplectic-toric manifold. Applications
to symplectic blowing up and the sympletic packing problem will also presented.
October 22
TBA
October
29
I will talk about joint work with H.Sati (University of Adelaide)
about the IIA and IIB string partition functions, and how their
investigation leads to elliptic cohomology. In the IIA case, a
W_7 anomaly discovered by Diaconescu-Moore-Witten is an obstruction
to orientability with respect to elliptic cohomology. This obstruction,
when refined to w_4 (or \lambda\in Z/24) becomes an obstruction
to orientability with respect to real elliptic cohomology (resp. tmf).
We construct a corresponding elliptic cohomology partition function,
and argue that it should reflect the 11 (or 12) dimensional limit
of IIA string theory. In IIB string theory, Diaconescu-Moore-Witten
point out a puzzle concerning modularity (S-duality) of the partition
function. We argue that the puzzle is not solvable by any type of
twisted K-theory, and argue, again, that the modularity is recovered
in elliptic cohomology. We present mathematical and physical arguments
and propose T-duality to the IIA treatment, as well as a possible
12-dimensional F-theory limit.
December 3
If R is an $S^1$-equivariant S-algebra, then there are Dyer-Lashof
operations in the homology of R, and hence in the spectral sequences
for the homology of the $S^1$-homotopy fixed points, Tate spectrum, and
homotopy orbits of R. We determine the behavior of differentials on
these operations. The intended application is to the $S^1$ and
$C_{p^k}$ fixed points of THH(R), for an S-algebra R. (This is joint
with John Rognes.)
November
12
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