2024/10/15 by Gorokhovsky, Alexander, van Erp, Erik
#46L80 (Primary) 58J20 #58J40 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2410.11982
In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal Heisenberg symbol, calculates the index. A crucial ingredient of our index formula was a new trace on the algebra of Heisenberg pseudodifferential operators. The construction of this trace was rather involved. In the present paper, we clarify the nature of this trace.