Comparison of motivic Chern classes and stable envelopes for cotangent bundles

Abstract

We consider a complex smooth projective variety equipped with an action of an algebraic torus with a finite number of fixed points. We compare the motivic Chern classes of Białynicki-Birula cells with the $K$-theoretic stable envelopes of cotangent bundle. We prove that under certain geometric assumptions satisfied e.g. by homogenous spaces these two notions coincide up to normalization.

arXiv commentAccepted for publication by the Journal of Topology