The Witten deformation of the Dolbeault complex

2020/07/31 by López, Jesús Álvarez, Gilkey, Peter
#58J20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.15889

Abstract

We introduce a Witten-Novikov type perturbation ∂_ω of the Dolbeault complex of any complex Kähler manifold, defined by a form ω of type (1,0) with ∂ω=0. We give an explicit description of the associated index density which shows that it exhibits a nontrivial dependence on ω. The heat invariants of lower order are shown to be zero.

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