# Some topological properties of quotients modulo semisimple algebraic groups

### R. V. Gurjar

Tata Institute of Fundamental Research, Bombay, India

## Abstract

We will prove a general result in Invariant Theory, viz. for a quotient ℂn//G, where G is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient ℂn//G is trivial and the local second homology group is finite. Using this we will prove that the completion of the local ring of any point in ℂn//G is a unique factorization domain (UFD).

## Cite this article

R. V. Gurjar, Some topological properties of quotients modulo semisimple algebraic groups. Comment. Math. Helv. 84 (2009), no. 4, pp. 793–806

DOI 10.4171/CMH/181