Abstract. We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order formula defining the family. As an important consequence, we derive that the number of distinct homotopy types of semi-algebraic subsets of Rk defined by a quantifier-free first order formula Φ, where the sum of the ad-ditive complexities of the polynomials appearing in Φ is at most a, is bounded by 2(k+a) O(1). This proves a conjecture made in [5]
An r-uniform hypergraph H is semi-algebraic of complexity t=(d,D,m) if the vertices of H correspond ...
Given a semi-algebraic set S, we study compactifications of S that arise from embeddings into comple...
A k-ary semi-algebraic relation E on ℝ_d is a subset of ℝ_(kd), the set of k-tuples of points in ℝ_(...
We prove a nearly optimal bound on the number of stable homotopy types occurring in a k-parameter se...
Abstract. In this paper we prove new bounds on the sum of the Betti numbers of closed semi-algebraic...
Given Q 2 R[X1 ; : : : ; Xk ] with deg(Q) d; we give an algorithm that outputs a semi-algebraic des...
This paper gives a description of some aspects of complexity in real algebraic geometry: explicit bo...
Let R be a real closed field, Q ⊂ R[Y1 , . . . , Yl, X1 , . . . , Xk], with degY(Q) ≤ 2, degX(Q) ≤ d,...
We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $...
AbstractWe define counting classes #PR and #PC in the Blum–Shub–Smale setting of computations over ...
International audienceLet R be a real closed field, Q subset of R[Y-1, ... , Y-l , X-1, ... , X-k], ...
In this thesis, we consider semi-algebraic sets over a real closed field R defined by quadratic poly...
A k-ary semi-algebraic relation E on R-d is a subset of R-kd, the set of k-tuples of points in R-d, ...
In this paper we give a new bound on the sum of the Betti numbers of closed semi-algebraic sets. Thi...
In this paper we prove new bounds on the sum of the Betti numbers of closed semi-algebraic sets and ...
An r-uniform hypergraph H is semi-algebraic of complexity t=(d,D,m) if the vertices of H correspond ...
Given a semi-algebraic set S, we study compactifications of S that arise from embeddings into comple...
A k-ary semi-algebraic relation E on ℝ_d is a subset of ℝ_(kd), the set of k-tuples of points in ℝ_(...
We prove a nearly optimal bound on the number of stable homotopy types occurring in a k-parameter se...
Abstract. In this paper we prove new bounds on the sum of the Betti numbers of closed semi-algebraic...
Given Q 2 R[X1 ; : : : ; Xk ] with deg(Q) d; we give an algorithm that outputs a semi-algebraic des...
This paper gives a description of some aspects of complexity in real algebraic geometry: explicit bo...
Let R be a real closed field, Q ⊂ R[Y1 , . . . , Yl, X1 , . . . , Xk], with degY(Q) ≤ 2, degX(Q) ≤ d,...
We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $...
AbstractWe define counting classes #PR and #PC in the Blum–Shub–Smale setting of computations over ...
International audienceLet R be a real closed field, Q subset of R[Y-1, ... , Y-l , X-1, ... , X-k], ...
In this thesis, we consider semi-algebraic sets over a real closed field R defined by quadratic poly...
A k-ary semi-algebraic relation E on R-d is a subset of R-kd, the set of k-tuples of points in R-d, ...
In this paper we give a new bound on the sum of the Betti numbers of closed semi-algebraic sets. Thi...
In this paper we prove new bounds on the sum of the Betti numbers of closed semi-algebraic sets and ...
An r-uniform hypergraph H is semi-algebraic of complexity t=(d,D,m) if the vertices of H correspond ...
Given a semi-algebraic set S, we study compactifications of S that arise from embeddings into comple...
A k-ary semi-algebraic relation E on ℝ_d is a subset of ℝ_(kd), the set of k-tuples of points in ℝ_(...
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