## Singular cotangent bundle reduction & Spin Calogero-Moser systems

### Simon Hochgerner

(University of Vienna)

**Abstract:**
Suppose a Riemannian configuration manifold $Q$ is acted upon by a compact
Lie group $K$ such that there is only a single isotropy type. The
cotangent lifted action by $K$ on $T^*Q$ is Hamiltonian with momentum map
$J$. We study the symplectically reduced space $J^{-1}(\orbit)/K$ where
$\orbit$ is a coadjoint orbit. This is a singular space which is
stratified into smooth symplectic pieces (in a technical sense). We are
able to give a description of the reduced space as a fibered product of
$T^*(Q/K)$ and a symplectic reduction of $\orbit$. Moreover, we
can give an explicit formula of the reduced symplectic form in terms
intrinsic to this fibered product description.
The talk will include some informal background on Hamiltonian
mechanics and singular symplectic reduction, and, if time permits, I will
discuss some examples.