Math Seminars.
Paul Feehan,
Witten's conjecture and gluing PU(2) monopoles.
We will discuss new results on gluing theory for PU(2) monopoles and
applications to the proof of Witten's conjecture on the relation between
the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. The
PU(2)-monopole moduli space provides a noncompact cobordism between links
of compact moduli spaces of U(1) monopoles of Seiberg-Witten type and the
(Donaldson) moduli space of anti-self-dual SO(3) connections, which appear
as singularities in this larger moduli space. The purpose of the gluing
theorem is to provide topological models for neighborhoods of ideal
Seiberg-Witten moduli spaces appearing in lower levels of the Uhlenbeck
compactification of the moduli space of PU(2) monopoles and thus permit
calculations of their contributions to Donaldson invariants using the
PU(2) monopole cobordism.