17 citations · 67 across the 30 of their papers we have counts for
31 papers
The unitary group in the strong topology and a construction of Dixmier-Douady
Nikolai V. Ivanov, Marina Prokhorova
By a theorem of Dixmier-Douady the unitary group of an infinite-dimensional separable Hilbert space in the strong operator topology is contractible. The Dixmier-Douady proof is…
Non-abelian cohomology and Seifert-Van Kampen theorem
Nikolai V. Ivanov
The first goal of the present paper it to present a simple and elementary proof of the standard Seifert-van Kampen theorem based on ideas of P. Olum. The key tool is the singular c…
Boundary triplets and the index of families of self-adjoint elliptic boundary problems
Nikolai V. Ivanov
The paper is devoted to an abstract axiomatic version of a construction of boundary triplets implicit in the works of M.I. Vishik and G. Grubb and its applications to the index of…
Scarf's theorems, simplices, and oriented matroids
Nikolai V. Ivanov
In 1967 Herbert Scarf suggested a new proof of Brouwer fixed point theorem based on a surprising analogue of Sperner's lemma. This analogue was motivated by Scarf's work in game th…
The index of self-adjoint Shapiro-Lopatinskii boundary problems of order one
Nikolai V. Ivanov
The paper is devoted to an analogue of Atiyah-Bott-Singer index theorem for families of self-adjoint elliptic (i.e. satisfying the Shapiro-Lopatinskii condition) local boundary pro…
Spectral sections: two proofs of a theorem of Melrose-Piazza
Nikolai V. Ivanov
Spectral sections of families of self-adjoint Fredholm operators were introduced by Melrose and Piazza for the needs of index theory. The basic result about spectral sections is a…