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On index theorems for linear ordinary differential operators

Michèle Loday-Richaud, Geneviève Pourcin (1997)

Annales de l'institut Fourier

We introduce and study the sheaf of Deligne to describe singular points of a linear differential operator D and we develop a technique based on homological algebra to prove index theorems for D .As particular cases, we obtain index theorems for D acting in spaces of multisummable series and a new proof of the index theorem of Malgrange in the space of convergent power series and of the index theorems of Ramis in the spaces of Gevrey series.We compute the values of these indices in terms of the formal...

On localization in holomorphic equivariant cohomology

Ugo Bruzzo, Vladimir Rubtsov (2012)

Open Mathematics

We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.

On symplectic cobordism of real projective plane.

Malkhaz Bakuradze (2000)

Publicacions Matemàtiques

This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements Θ2i+1(2) in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.

On the Bézout equation in the ring of periodic distributions

Rudolf Rupp, Amol Sasane (2016)

Topological Algebra and its Applications

A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.

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