This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
7.6 Bibliographical Notes
N. Alon, Tools from higher algebra, Handbook of combinatorics, 1749–1783, Elsevier, Amsterdam (1995).
S. Basu, On different bounds on different Betti numbers, Discrete and Computational Geometry, 30:1, 65–85, (2003).
S. Basu, On Bounding the Betti Numbers and Computing the Euler Characteristics of Semi-algebraic Sets, Discrete and Computational Geometry, 22 1–18 (1999).
S. Basu, R. Pollack, M.-F. Roy, On the number of cells defined by a family of polynomials on a variety, Mathematika, 43 120–126 (1996).
S. Basu, R. Pollack, M.-F. RoyOn the Betti Numbers of Sign Conditions, Proc. Amer. Math. Soc. 133, 965–974 (2005).
G.D. Birkhoff, Collected Mathematical Papers, Vol II, Amer. Math. Soc., New York (1950).
A. Gabrielov, N. Vorobjov, Betti Numbers for Quantifier-free Formulae. Discrete and Computational Geometry, 33 395–401 (2005).
Ham, Le, Un theoreme de Zariski du type de Lefschetz, Ann. Sc. Ec. Norm. Sup., (3) vol 6. 317–355 (1973).
Ham, Le, Lefschetz theorems on quasi-projective varieties, Bull. Soc. Math. France, 113, 123–142 (1985).
J. Milnor, On the Betti numbers of real varieties, Proc. AMS 15, 275–280 (1964).
M. Morse, Relations between the critical points of a real function of n independent variables, Trans. Amer. Math. Soc., 27 345–396 (1925).
O. A. Oleinik, Estimates of the Betti numbers of real algebraic hypersurfaces, Mat. Sb. (N.S.), 28(70): 635–640 (Russian) (1951).
O. A. Oleinik, I. B. Petrovskii, On the topology of real algebraic surfaces, Izv. Akad. Nauk SSSR 13, 389–402 (1949).
R. Thom, Sur l’homologie des variétés algébriques réelles, Differential and Combinatorial Topology, 255–265. Princeton University Press, Princeton (1965).
H.E. Warren, Lower bounds for approximations by non-linear manifolds, Trans. Amer. Math. Soc. 1333, 167–178, (1968).
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2006). Quantitative Semi-algebraic Geometry. In: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics, vol 10. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33099-2_8
Download citation
DOI: https://doi.org/10.1007/3-540-33099-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33098-1
Online ISBN: 978-3-540-33099-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)