Betti Numbers of Semialgebraic and Sub‐Pfaffian Sets

By Andrei Gabrielov, Nicolai N. Vorobjov, T. Zell. 2004

50 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4b7ea9baa5982971edd33cefeb578014ef695637

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Nicolai N. Vorobjov
2. Andrei Gabrielov

In Geometry and Topology

1. Nicolai N. Vorobjov
2. Andrei Gabrielov

In Mathematical Physics

1. Nicolai N. Vorobjov
2. Andrei Gabrielov

Citations in the corpus

• Approximation of definable sets by compact families, and upper bounds on homotopy and homology (2007, methodology): “Based on this construction, we refine the results from [9, 10] and prove similar upper bounds, individually for different Betti numbers, for images under arbitrary continuous definable maps.”
• Complexity of computations with Pfaffian and Noetherian functions (2004, background): “Theorem 3.1 implies various upper bounds on the topological complexity of a semi-Pfaffian set as functions of the format by applying almost without change some well-developed techniques for semialgebraic sets.”