Betti numbers of nilmanifolds associated with path graphs

Abstract: Given a finite graph G, Dani and Mainkar associate with it a two-step nilpotent Lie algebra L(G), as well as a compact nilmanifold N(G). By a theorem of Nomizu, the de Rham cohomology of N(G) is isomorphic to the Lie algebra cohomology of L(G). In joint work with Marco Aldi, Samuel Bevins, Sergio Da Silva, Quincy Frias, and Tomás Mejía Gómez, we use Lie-algebraic methods to calculate the Betti numbers of all Dani-Mainkar nilmanifolds associated with path graphs. To assist with our computations, we develop a graphical calculus for the Chevalley-Eilenberg complex of the Lie algebra associated with any path graph.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the topic

VCU Geometry and Topology Seminar

Series comments: Research seminar on Geometry and Topology at Virginia Commonwealth University