For closed manifolds, signature of the intersection form on cohomology is an important topological invariant. It is expressed as the index of the signature operator, and index theoretical approach has been very successful,for example to understand higher signature invariants.

On stratified pseudomanifolds, we consider the intersection cohomology, and generalizations of signature have been studied by many authors. From index theoretical viewpoint, there has also been works to analyze signature operators on such spaces, and also to construct higher signature index classes in this context.

In this talk, focusing on the case of manifolds with edges satisfying the Witt condition, I will explain my ongoing work to give a topological approach to understand the indices of such operators.

I will give a special class of perturbations of signature operators on such spaces, and show that the index invariants gained from it coincides with the known signature invariants. Further I will explain how this new definition avoids analytic

difficulties with usual signature operators on singular spaces.