Combinatorial complexity in o-minimal geometry

Combinatorial complexity in o-minimal geometry (2009)

Cached

Download Links

[www.math.purdue.edu]

by Saugata Basu

BibTeX

@MISC{Basu09combinatorialcomplexity,
    author = {Saugata Basu},
    title = {Combinatorial complexity in o-minimal geometry},
    year = {2009}
}

Bookmark

OpenURL

Abstract

Citations

183	den Dries. Tame Topology and O-minimal Structures - van - 1998
113	On the Betti Numbers of Real Varieties - Milnor - 1964
85	Definable sets in ordered structures - Pillay, Steinhorn - 1986
80	Sur l’homologie des varietes algebriques reelles, Differential and Combinatorial - Thom - 1965
77	Geometric Categories and O-minimal Structures - Dries, Miller - 1996
77	Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function - Wilkie - 1996
76	Using the Borsuk-Ulam Theorem - Matouˇsek - 2003
58	Real quantifier elimination is doubly exponential - Davenport, Heintz - 1988
40	Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete (3 - Bochnak, Coste, et al. - 1987
39	Petrovskii On the topology of real algebraic surfaces - Oleinik, B - 1949
31	A theorem of the complement and some new o-minimal structures - Wilkie - 1999
28	Lectures on discrete geometry, Graduate Texts - Matouˇsek - 2002
28	Wilkie Quasianalytic Denjoy-Carleman classes and ominimality - Rolin, Speissegger, et al. - 2003
26	The field of reals with multisummable series and the exponential function - Dries, Speissegger
21	The real field with convergent generalized power series is model commplete and o-minimal - Dries, Speissegger - 1998
19	Betti numbers of semialgebraic and sub-Pfaffian sets - Gabrielov, Vorobjov, et al.
17	Complexity of computations with Pfaffian and Noetherian functions - Gabrielov, Vorobjov - 2004
16	On the combinatorial and topological complexity of a single cell, Discrete and Computational Geometry - Basu - 2003
16	Betti Numbers of semialgebraic sets defined by quantifier-free formulae, Discrete Comput - Gabrielov, Vorobjov - 2005
15	Sharir Crossing patterns of Semi-algebraic Sets - Alon, Pach, et al. - 2005
15	On the Betti numbers of sign conditions - Basu, Pollack, et al.
14	Arrangements and their applications, Handbook of computational geometry - Agarwal, Sharir - 2000
14	On different bounds on different Betti numbers of semi-algebraic sets - Basu - 2003
14	Complexity of cylindrical decompositions of sub-Pfaffian sets - Gabrielov, Vorobjov - 2001
13	M.-F.: Algorithms in Real Algebraic Geometry - Basu, Pollack, et al. - 2006
11	Complements of subanalytic sets and existential formulas for analytic functions - Gabrielov - 1996
8	Poset fiber theorems - Bjorner, Wachs, et al.
5	Geometric range searching and its relatives, Advances in discrete and computational geometry (South - Agarwal, Erickson - 1996
5	Comparison theorems for o-minimal singular (co)homology’, Trans - Edmundo, Woerheide
4	number bounds, applications and algorithms - Basu, Pollack, et al. - 2005
4	Approximation of definable sets by compact families and upper bounds on homotopy and homology, preprint at arXiv:math.AG/0710.3028v1 - Gabrielov, Vorobjov
3	Computing the first Betti number of a semi-algebraic set - Basu, Pollack, et al.
2	o-minimal Čech cohomology - Edmundo, Peatfield
1	An introduction to o-minimal geometry’, Dottorato di Ricerca - Coste - 2000