26 citations · 42 across the 14 of their papers we have counts for
8 papers · 1 filter
An exponential Lojasiewicz inequality for semi-Pfaffian sets
Nicolai Vorobjov
We prove a generalization of the version, due to A. Gabrielov, of the Łojasiewicz inequality for not necessarily restricted semi-Pfaffian sets. Unlike the most variants of the Łoja…
Complexity of deciding whether a tropical linear prevariety is a tropical variety
Dima Grigoriev, Nicolai Vorobjov
We give an algorithm, with a singly exponential complexity, deciding whether a tropical linear prevariety is a tropical linear variety. The algorithm relies on a criterion to be a…
Upper bounds on Betti numbers of tropical prevarieties
Dima Grigoriev, Nicolai Vorobjov
We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum o…
On irreducible components of real exponential hypersurfaces
Cordian Riener, Nicolai Vorobjov
Fix any algebraic extension of the field of rationals. In this article we study exponential sets . Such sets are described by the vani…
Triangulations of monotone families I: Two-dimensional families
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
Let be a compact definable set in an o-minimal structure over , e.g., a semi-algebraic or a subanalytic set. A definable family $\{ S_δ|\> 0< δ…
Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to clos…
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
Andrei Gabrielov, Nicolai Vorobjov
We prove new upper bounds on homotopy and homology groups of o-minimal sets in terms of their approximations by compact o-minimal sets. In particular, we improve the known upper bo…
On the number of homotopy types of fibres of a definable map
Saugata Basu, Nicolai Vorobjov
In this paper we prove a single exponential upper bound on the number of possible homotopy types of the fibres of a Pfaffian map, in terms of the format of its graph. In particular…