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Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials

Abstract:
Let R be a real closed field, Q ⊂ R[Y1 , . . . , Yl, X1 , . . . , Xk], with degY(Q) ≤ 2, degX(Q) ≤ d, Q ∈ Q, #(Q) = m, and P ⊂ R[X1, . . . , Xk] with degX(P) ≤ d, P ∈ P, #(P) = s, and S ⊂ Rl+k a semi-algebraic set defined by a Boolean formula without negations, with atoms P = 0, P ≥ 0, P ≤ 0, P ∈ P ∪ Q. We prove that the sum of the Betti numbers of S is bounded by l2 (O(s + l + m)ld)k+2m.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/JEMS/208

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Institution:
University of Oxford
Division:
MPLS
Department:
Computer Science
Role:
Author
Publisher:
European Mathematical Society
Journal:
Journal of the European Mathematical Society More from this journal
Volume:
12
Issue:
2
Pages:
529–553
Publication date:
2010-03-16
DOI:
EISSN:
1095-7189
ISSN:
1052-6234
Keywords:
Pubs id:
pubs:446347
UUID:
uuid:cccb7759-682e-4dda-827f-73cf63d12fe5
Local pid:
info:fedora/pubs:446347
Source identifiers:
446347
Deposit date:
2016-07-28

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