Output details
11 - Computer Science and Informatics
University of Bath
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Article title
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
Type
D - Journal article
Title of journal
Journal of the London Mathematical Society
Article number
-
Volume number
80
Issue number
1
First page of article
35
ISSN of journal
0024-6107
Year of publication
2009
Number of additional authors
1
Additional information
<13>We establish new singly-exponential upper bounds on the topology (more precisely, Betti-numbers) of semi-algebraic and sub analytic sets, and essentially closes the problem of upper bounds. The importance of this topic to mathematics is explained in [Arnold, Russ. Math. Surv. 2002, 57, 833.] The new technique used in our proof has independent interest, for example in establishing real analogue of Toda's theorem [Basu, Zell, Found. Comput. Math., 10, 2010]. The weaker results, obtained previously by authors, are widely known and used: see [Basu, Pollack, Roy, Algorithms in Real Algebraic Geometry, 2nd ed., Springer, 2006].
Interdisciplinary
-
Cross-referral requested
-
Research group
A - Mathematical Foundations
Citation count
2
Proposed double-weighted
No
Double-weighted statement
-
Reserve for a double-weighted output
No
Non-English
No
English abstract
-
