8 papers · 1 filter
Symplectic reduction along a submanifold
Peter Crooks, Maxence Mayrand
We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of…
On the singularities of Mishchenko-Fomenko systems
Peter Crooks, Markus Röser
To each complex semisimple Lie algebra and regular element , one associates a Mishchenko-Fomenko subalgebra $\mathcal{F}_a\subseteq\ma…
Towards a quantization of the double via the enhanced symplectic category
Peter Crooks, Jonathan Weitsman
This paper considers the enhanced symplectic "category" for purposes of quantizing quasi-Hamiltonian -spaces, where is a compact simple Lie group. Our starting point is the…
The log symplectic geometry of Poisson slices
Peter Crooks, Markus Röser
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-se…
Hessenberg varieties and Poisson slices
Peter Crooks, Markus Röser
This work pursues a circle of Lie-theoretic ideas involving Hessenberg varieties, Poisson geometry, and wonderful compactifications. In more detail, one may associate a symplectic…
On the fibres of Mishchenko-Fomenko systems
Peter Crooks, Markus Röser
This work is concerned with Mishchenko and Fomenko's celebrated theory of completely integrable systems on a complex semisimple Lie algebra . Their theory associates…