Moduli Space of General Connections

TL;DR

This paper studies the local invariants of general connections with torsion, calculates the dimensions of their moduli spaces, and demonstrates the rationality of their Poincaré series, confirming a classical finiteness property.

Contribution

It provides explicit calculations of moduli space dimensions and constructs the Poincaré series, extending the understanding of invariants of general connections with torsion.

Findings

Dimensions of moduli spaces are explicitly calculated.

Poincaré series of the geometric structure is shown to be rational.

Finiteness of invariants as per Tresse's assertion is confirmed.

Abstract

We consider local invariants of general connections (with torsion). The group of origin-preserving diffeomorphisms acts on a space of jets of general connections. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of connection is constructed, and shown to be a rational function, confirming the finiteness assertion of Tresse.