Register for: AustMS2017

Details of talk

TitleThe $K$-theory of loop spaces and elliptic cohomology
PresenterMatthew James Spong (The University of Melbourne)
Author(s)Mr Matthew James Spong
SessionCategory Theory, Algebraic Topology, K-Theory
Time16:00:00 2017-12-13

Let $T$ be a torus. In 1994 Ian Grojnowski gave a construction of a
$T$-equivariant elliptic cohomology theory associated to an elliptic curve over
the complex numbers. However, as noted by Grojnowski himself, this construction
is somewhat ad hoc and unwieldy to work with. Let $M$ be a $T$-space and $LM$
the space of free loops in $M$, so that there is an action of $LT$ on $LM$,
where $LT$ is the group of free loops in the torus. Based on work of Nitya
Kitchloo, we construct a version of equivariant $K$-theory for $LT$-spaces, and
show that the $LT$-equivariant $K$-theory of $LM$ is isomorphic to Grojnowski's
theory on the $T$-space $M$. Since the loop space construction is motivated by
the idea of fields on a circle, this suggests a physical interpretation of
Grojnowski's theory.