TETRAHEDRAL GEOMETRY/TOPOLOGY SEMINAR
ANNOUNCEMENT
DATE: Friday, September
14, 2007
LOCATION: Hempfield
High School, Room 213 (directions at http://www.millersville.edu/~tgts/)
followed by
dinner at a place to be determined.
4:30 TALK: John
Carter,
“Non-loopable K-theory equivalences”
Over the summer I
explored and extended a family of non-loopable
K-theory equivalences
constructed by Lisa Langsetmo and Don Stanley in 2000. I will talk about why
this is an
interesting family of spaces
and how I extended their results. A
K-theory equivalence is a
map of spaces f : X à Y such that
K(X)=K(Y). A non-loopable
equivalence is one such
that K(\Omega X) \neq K(\Omega Y). In
ordinary homology, given a homology equivalence
of 1-connected
spaces, there is a homology equivalence of loop spaces. But for K-theories
and non-connective
homology theories the story is different.
There are spaces such that
K-theory can
'see' the loop space but not the space.
This is interesting not only for what it
says about what
K-theory sees but also for what it says about methods for constructing loop
spaces. (Fair warning, I will say spectral sequence a
number of times during this talk.)
EVERYONE WELCOME
PLEASE FORWARD THIS ANNOUNCEMENT TO ANYONE
INTERESTED
The Tetrahedral Geometry/Topology Seminar is
sponsored jointly by