Intrinsic characteristic classes for a local Lie group

TL;DR

This paper introduces odd order cohomology classes for local Lie groups, identifying obstructions to their globalizability and relating one class to the Godbillon-Vey class, highlighting their secondary nature when curvature vanishes.

Contribution

It defines new cohomology classes for local Lie groups and connects them to known geometric invariants, providing insights into their globalizability.

Findings

First class obstructs globalizability.

Third class relates to Godbillon-Vey class.

Classes are secondary, emerging when curvature vanishes.

Abstract

For a local Lie group M we define odd order cohomology classes. The first class is an obstruction to globalizability of the local Lie group. The third class coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.