## Dr. Nathan Perlmutter

Stanford University

Guestuniversity: Universität Augsburg

Guestperiod: July 2017

E-mail: nperlmut(at)stanford.edu

Homepage: https://web.stanford.edu/~nperlmut/

## Publications within SPP2026

We develop an algebro-analytic framework for the systematic study of the continuous bounded cohomology of Lie groups in large degree. As an application, we examine the continuous bounded cohomology of PSL(2,R) with trivial real coefficients in all degrees greater than two. We prove a vanishing result for strongly reducible classes, thus providing further evidence for a conjecture of Monod. On the cochain level, our method yields explicit formulas for cohomological primitives of arbitrary bounded cocycles.

**Related project(s):****27**Invariants and boundaries of spaces

We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove a vanishing theorem for the continuous bounded cohomology of SL(2,R) in degree 4, establishing a special case of a conjecture of Monod.

Journal | Geometry & Topology |

Volume | 19 |

Pages | 3603–3643 |

Link to preprint version | |

Link to published version |

**Related project(s):****27**Invariants and boundaries of spaces