I will describe the 'HOLONOMY GROUP' of smooth curves and smooth
projective varieties as a generalization of Fundamental Group. This was carried out in the past jointly with Indrani Biswas, S. Subramanian and V. Balaji through a series of papers. Then we define it for integral curves. Then we explain the relation between (strongly) stable bundles and irreducible representations of these groups.
This is a joint work Usha Bhosle. Recently, with Usha Bhosle and Sanjay Sigh, it was further generalized to Hitchin pairs on an integral curve and defined a more general Holonomy groups.
