Week 1 - Organizational Meeting, Friday April 4th, 10 AM Gilkey 104
Week 2 - Tuesday, April 8th, 12:00, Gilkey 115
Jacob Landeros, Whitehead Automorphisms
Week 3 - Tuesday, April 15th, Gilkey 115
Carolyn McCaffrey , The Borsuk Ulam Theorem and the Brouwer Fixed Point Theorem
Week 4 - Friday, April 25th, Gilkey 104
Mark Walsh, University of Oregon
Isotopy and Concordance in the Space of Metrics of Positive Scalar Curvature
The problem of whether or not a smooth closed manifold X admits a Riemannian
metric of positive scalar curvature (psc-metric) has been extensively studied and is
now largely understood. In the case where X admits such a metric we may ask
about the topology of the space Riem+(X) consisting of all psc-metrics on
X. In general, very little is known about the topology of this space, even at the level
of path-connectedness. One interesting problem concerns the topological notions of
isotopy and concordance (pseudo-isotopy) when applied to this space. It is known
that isotopic psc-metrics are concordant. Whether or not the converse holds is an
open question. In this talk we will discuss a theorem which states that for a certain
type of concordance, constructed using the surgery techniques of Gromov and
Lawson, this converse does indeed hold.
Week 5 - Tuesday, April 29th, Gilkey 115
Lorenz Schwachhoefer, University of Dortmund, Manifolds with lower curvature bounds continued
Week 6 - Tuesday, May 6th, Gilkey 115
Aaron Leeman, University of Oregon
Generating spaces for K-theory acyclics
Abstract:
I will consider a functor L_H(-) from the category of “nice” topological spaces to itself. This functor satisfies
several important qualities, but one of them is that it turns maps that induce an isomorphism with respect to
integral homology into homotopy equivalences. In fact, I will call the above functor “localization with respect
to integral homology.” It’s intended to be analogous to localization in a ring, instead of inverting certain elements
we invert certain maps.
It turns out one can do such a thing for any generalized homology theory, but I’ll be considering mainly
L_K(-), which is localization with respect to complex K-theory. To investigate such a thing, it’s natural to
ask which spaces are sent by this functor to something contractible. I’ll discuss a result by Emmanuel
Dror-Farjoun along these lines and work I’ve been doing in this area.
Week 7 - Tuesday, May 13th, Gilkey 115
Jeremiah Heller, Homotopy theory and Algebraic Geometry
Week 8 - Tuesday, May 20th, Gilkey 115
Bill Kronholm, Introduction to Equivariant Topology.
Abstract: The study of symmetries of topological spaces can be approached by considering the action of a group
on the space. In this equivariant setting, we can study homotopy, homology, and cohomology, each of which
has a slightly different feel than in the usual nonequivariant setting.
In my work, I consider the action of the group Z/2Z on spaces and study their cohomology.
In this talk, I'll show some of my computations of the equivariant cohomology of real projective spaces and Grassmann manifolds.
Week 9 - Tuesday, May 27th, Gilkey 115
No talk this week due to the Lonseth Lecture.
Week 10 - Tuesday, June 3rd, Gilkey 115
Winter: Winter Term - 12:00 - 12:50 in Kidder 238
Week 1 - Tuesday, January 8th
No Tuesday seminar this week.
Week 2 - Tuesday, January 15th
Shari Ultman
Cohomogeneity one manifolds; the double-disk construction and cohomology
(Continued from previous talk.)
Week 3 - Tuesday, January 22nd
Christine Escher
Topological methods for manifolds of positive sectional curvature.
Week 4 - Tuesday, January 29nd
Christine Escher
Topological methods for manifolds of positive sectional curvature.(continued)
Week 5 - Tuesday, February 5th,
Dennis Garity
Intersection of Tori in R^3
Week 6 - Tuesday, February 12th,
Dennis Garity
Intersection of Tori in R^3, continued
Week 7 - Tuesday, February 19th,
Aniruth Phon-On
Morton Brown's Proof of the Generalized Schonflies Theorem
Week 8 - Tuesday, February 26th,
Organizational
Friday, February 29th, Colloquium, 4 PM
Dusan Repovs
The Bing-Borsuk and the Busemann Conjectures
We shall present a survey of two classical conjectures concerning the characterization of manifolds:
the Bing Borsuk Conjecture asserts that every n-dimensional homogeneous ANR is a topological
n-manifold, whereas the Busemann Conjecture asserts that every n-dimensional G-space is a
topological n-manifold. The key object in both cases are so-called generalized manifolds, i.e. ENR homology manifolds.
We shall look at their history, from the early beginnings in 1930's to the present day, concentrating on those geometric
properties of these spaces which are particular for dimensions 3 and 4, in comparison with generalized (n>4)-manifolds.
In the second part of the talk we shall present the current state of the two conjectures (the work of Bing-Borsuk,
Bestvina-Daverman-Venema-Walsh, Brahm, Bryant-Ferry-Mio-Weinberger, Busemann, Cannon, Daverman-Repovs,
Daverman-Thickstun, Halverson-Repovs, Edwards, Krakus, Lacher-Repovs, Pedersen-Quinn-Ranicki, Thurston,
and others). We shall also list open problems and related conjectures.
Week 9- Tuesday, March 4th,
Paul Synhavsky
A Topological Proof of Grushko's Theorem
Fall: (Archive of Seminars, Fall term 2007)
Week 1 - Sep 25, 2007,
Organizational Meeting
Week 2 - Oct 2, 2007,
William A. Bogley,
Problems in Low Dimensional Topology
Week 3 - Oct 9, 2007,
Dennis J. Garity,
Hopf Theorems
Week 4 - Oct. 16, 2007,
Jeremy Hoehn,
Spectral Sequences
Week 5 - Oct. 23, 2007,
A. Jacob Landeros,
Curves with One Self Intersection on Punctured Genus n Tori
Week 6 - Oct. 30, 2007,
Dean Wills,
Sperner's Lemma and the Brouwer Fixed Point Theorem
Week 7 - Nov. 6, 2007,
Aniruth Phon-On,
Upper Semi Continuous Decompositions and the Monotone Light Factorization Theorem
Week 8 - Nov. 13, 2007
Shari Ultman
Cohomogeneity one manifolds; the double-disk construction and cohomology
A current problem in geometry is the attempt to understand the apparent scarcity
of examples of manifolds with positive sectional curvature. One approach is to
study manifolds of non-negative curvature. A cohomogeneity one manifold--
that is: a closed, connected, smooth manifold with a smooth action by a compact
Lie group resulting in a one-dimensional orbit space--often admits non-negative
curvature. In this case, the manifold is diffeomorphic to the union of two disk
bundles glued together along their boundaries. This double-disk construction
can then be used to study the topology of the manifold.
Week 9 - Nov. 20, 2007
Shari Ultman
Cohomogeneity one manifolds; the double-disk construction and cohomology, (continued)
Week 10 - Nov. 27, 2007
Week 1 -
Week 2 -
Tuesday, May 20th, Jeremiah Heller, Homotopy theory and Algebraic Geometry)