# 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.

## Key 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.