53 citations · 124 across the 21 of their papers we have counts for
8 papers · 1 filter
Thick morphisms of supermanifolds, quantum mechanics, and spinor representation
Hovhannes Khudaverdian, Theodore Voronov
"Thick" or "microformal" morphisms of supermanifolds generalize ordinary maps. They were discovered as a tool for homotopy algebras. Namely, the corresponding pullbacks provide $L_…
Odd Symmetric Tensors, and an Analogue of the Levi-Civita Connection for an Odd Symplectic Supermanifold
H. M. Khudaverdian, M. Peddie
We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank (non-degenerate) contravariant tensor field. We describe the difference be…
Odd Laplacians: geometrical meaning of potential, and modular class
H. M. Khudaverdian, M. Peddie
A second order self-adjoint operator is uniquely defined by its principal symbol and potential if it acts on half-densities. We analyse the potential …
Operator pencil passing through a given operator
A. Biggs, H. M. Khudaverdian
Let be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold . One can consider a pencil of operators $\hPi(Δ)=\{Δ_ł\}$ passi…
A short proof of the Buchstaber-Rees theorem
H. M. Khudaverdian, Th. Th. Voronov
We give a short proof of the Buchstaber-Rees theorem concerning symmetric powers. The proof is based on the notion of a formal characteristic function of a linear map of algebras.
Operators on superspaces and generalizations of the Gelfand-Kolmogorov theorem
H. M. Khudaverdian, Th. Th. Voronov
(Write-up of a talk at the Bialowieza meeting, July 2007.) Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological space can be canonically embedded into the…
Tube formula, Berezinians, and Dwork formula
Hovhannes M. Khudaverdian
We consider an example of tubes of hypersurfaces in Euclidean space and generalise the tube formula to supercase. By this we assign to a point of the hypersurface in superspace a r…
New Facts about Berezinians
Hovhannes M. Khudaverdian, Theodore Th. Voronov
We consider a new formula for Berezinian (superdeterminant). The Berezinian of a supermatrix is expressed as the ratio of polynomial invariants of . This formula follows fro…