{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T10:48:25Z","timestamp":1649069305417},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,3,7]],"date-time":"2008-03-07T00:00:00Z","timestamp":1204848000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2008,10]]},"DOI":"10.1007\/s00454-008-9070-1","type":"journal-article","created":{"date-parts":[[2008,3,6]],"date-time":"2008-03-06T10:20:37Z","timestamp":1204798837000},"page":"430-443","source":"Crossref","is-referenced-by-count":0,"title":["Topological Complexity of the Relative Closure of\u00a0a\u00a0Semi-Pfaffian\u00a0Couple"],"prefix":"10.1007","volume":"40","author":[{"given":"Thierry","family":"Zell","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,3,7]]},"reference":[{"key":"9070_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00009443","volume":"22","author":"S. Basu","year":"1999","unstructured":"Basu, S.: On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets. Discrete Comput. Geom. 22, 1\u201318 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"9070_CR2","unstructured":"Basu, S., Zell, T.: On projections of semi-algebraic sets defined by few quadratic inequalities. Arxiv: AG\/0602398"},{"key":"9070_CR3","volume-title":"G\u00e9om\u00e9trie Alg\u00e9brique R\u00e9elle","author":"J. Bochnak","year":"1987","unstructured":"Bochnak, J., Coste, M., Roy, M.-F.: G\u00e9om\u00e9trie Alg\u00e9brique R\u00e9elle. Springer, Berlin (1987). Revised 2nd edition in English: Springer (1998)"},{"key":"9070_CR4","unstructured":"Coste, M.: An introduction to o-minimal geometry. Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, 2000. Also available on http:\/\/www.ihp-raag.org\/"},{"key":"9070_CR5","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02685881","volume":"44","author":"P. Deligne","year":"1974","unstructured":"Deligne, P.: Th\u00e9orie de Hodge III. Publ. Math. IHES 44, 5\u201377 (1974)","journal-title":"Publ. Math. IHES"},{"key":"9070_CR6","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/s00209-003-0607-y","volume":"246","author":"D. Dugger","year":"2004","unstructured":"Dugger, D., Isaksen, D.: Topological hypercovers and $\\mathbb{A}^{1}$ -realizations. Math. Z. 246, 667\u2013689 (2004)","journal-title":"Math. Z."},{"key":"9070_CR7","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/PL00009371","volume":"19","author":"A. Gabrielov","year":"1998","unstructured":"Gabrielov, A.: Frontier and closure of a semi-Pfaffian set. Discrete Comput. Geom. 19, 605\u2013617 (1998)","journal-title":"Discrete Comput. Geom."},{"key":"9070_CR8","series-title":"Algorithms and Combinatorics","volume-title":"Discrete and Computational Geometry: The Goodman-Pollack Festschrift","author":"A. Gabrielov","year":"2003","unstructured":"Gabrielov, A.: Relative closure and the complexity of Pfaffian elimination. In: Discrete and Computational Geometry: The Goodman-Pollack Festschrift. Algorithms and Combinatorics, vol.\u00a025. Springer, Berlin (2003)"},{"key":"9070_CR9","doi-asserted-by":"crossref","unstructured":"Gabrielov, A.: Counter-examples to quantifier elimination for fewnomial and exponential expressions, Preprint (July 2006)","DOI":"10.17323\/1609-4514-2007-7-3-453-460"},{"key":"9070_CR10","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF02570696","volume":"14","author":"A. Gabrielov","year":"1995","unstructured":"Gabrielov, A., Vorobjov, N.: Complexity of stratifications of semi-Pfaffian sets. Discrete Comput. Geom. 14, 71\u201391 (1995)","journal-title":"Discrete Comput. Geom."},{"key":"9070_CR11","series-title":"NATO Science Series II","volume-title":"Normal Forms, Bifurcations and Finiteness Problems in Differential Equations","author":"A. Gabrielov","year":"2004","unstructured":"Gabrielov, A., Vorobjov, N.: Complexity of computations with Pfaffian and Noetherian functions. In: Ilyashenko, Y., Rousseau, C. (eds.) Normal Forms, Bifurcations and Finiteness Problems in Differential Equations. NATO Science Series II, vol. 137. Kluwer Academic, Dordrecht (2004)"},{"key":"9070_CR12","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s00454-004-1105-7","volume":"33","author":"A. Gabrielov","year":"2005","unstructured":"Gabrielov, A., Vorobjov, N.: Betti numbers for quantifier-free formulae. Discrete Comput. Geom. 33, 395\u2013401 (2005)","journal-title":"Discrete Comput. Geom."},{"key":"9070_CR13","series-title":"DIMACS: Series in Discrete Mathematics and Theoretical Computer Science","volume-title":"Algorithmic and Quantitative Real Algebraic Geometry","author":"A. Gabrielov","year":"2003","unstructured":"Gabrielov, A., Zell, T.: On the number of connected components of the relative closure of a semi-Pfaffian family. In: Algorithmic and Quantitative Real Algebraic Geometry. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol.\u00a060. American Mathematical Society, Providence (2003)"},{"key":"9070_CR14","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1112\/S0024610703004939","volume":"69","author":"A. Gabrielov","year":"2004","unstructured":"Gabrielov, A., Vorobjov, N., Zell, T.: Betti numbers of semialgebraic and sub-Pfaffian sets. J. Lond. Math. Soc. 69, 27\u201343 (2004)","journal-title":"J. Lond. Math. Soc."},{"key":"9070_CR15","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s000290050055","volume":"5","author":"M. Karpinski","year":"1999","unstructured":"Karpinski, M., Macintyre, A.: A generalization of Wilkie\u2019s theorem of the complement, and an application to Pfaffian closure. Selecta Math. (N.S.) 5, 507\u2013516 (1999)","journal-title":"Selecta Math. (N.S.)"},{"key":"9070_CR16","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/088","volume-title":"Fewnomials","author":"A.G. Khovanskii","year":"1991","unstructured":"Khovanskii, A.G.: Fewnomials. American Mathematical Society, Providence (1991)"},{"key":"9070_CR17","doi-asserted-by":"crossref","first-page":"93","DOI":"10.5802\/afst.891","volume":"7","author":"J.-M. Lion","year":"1998","unstructured":"Lion, J.-M., Rolin, J.-P.: Volumes, Feuilles de Rolle de Feuilletages analytiques et Th\u00e9or\u00e8me de Wilkie. Ann. Fac. Sci. Toulouse Math. 7, 93\u2013112 (1998)","journal-title":"Ann. Fac. Sci. Toulouse Math."},{"key":"9070_CR18","unstructured":"Lion, J.-M., Speissegger, P.: The theorem of the complement for sub-Pfaffian sets. Preprint. Available at http:\/\/www.math.mcmaster.ca\/~speisseg\/"},{"key":"9070_CR19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF01613615","volume":"7","author":"J.L. Monta\u00f1a","year":"1996","unstructured":"Monta\u00f1a, J.L., Morais, J.E., Pardo, L.M.: Lower bounds for arithmetic networks\u00a0II: Sum of Betti numbers. Appl. Algebra Eng. Commun. Comput. 7, 41\u201351 (1996)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"1","key":"9070_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1916-1501027-1","volume":"17","author":"W. Osgood","year":"1916","unstructured":"Osgood, W.: On functions of several complex variables. Trans. Am. Math. Soc. 17(1), 1\u20138 (1916)","journal-title":"Trans. Am. Math. Soc."},{"key":"9070_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9322-1","volume-title":"Algebraic Topology","author":"E. Spanier","year":"1981","unstructured":"Spanier, E.: Algebraic Topology. Springer, New York (1981)"},{"key":"9070_CR22","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1515\/crll.1999.508.189","volume":"508","author":"P. Speissegger","year":"1999","unstructured":"Speissegger, P.: The Pfaffian closure of an o-minimal structure. J. Reine Angew. Math. 508, 189\u2013211 (1999)","journal-title":"J. Reine Angew. Math."},{"key":"9070_CR23","series-title":"LMS Lecture Note Series","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511525919","volume-title":"Tame Topology and o-Minimal Structures","author":"L. den Dries van","year":"1998","unstructured":"van den Dries, L.: Tame Topology and o-Minimal Structures. LMS Lecture Note Series, vol.\u00a0248. Cambridge University Press, Cambridge (1998)"},{"key":"9070_CR24","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s000290050052","volume":"5","author":"A.J. Wilkie","year":"1999","unstructured":"Wilkie, A.J.: A theorem of the complement and some new o-minimal structures. Selecta Math. (N.S.) 5, 397\u2013421 (1999)","journal-title":"Selecta Math. (N.S.)"},{"key":"9070_CR25","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0022-4049(99)00017-1","volume":"139","author":"T. Zell","year":"1999","unstructured":"Zell, T.: Betti numbers of semi-Pfaffian sets. J. Pure Appl. Algebra 139, 323\u2013338 (1999). Effective methods in algebraic geometry (Saint-Malo, 1998)","journal-title":"J. Pure Appl. Algebra"},{"key":"9070_CR26","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s00454-004-1112-8","volume":"33","author":"T. Zell","year":"2005","unstructured":"Zell, T.: Topology of definable Hausdorff limits. Discrete Comput. Geom. 33, 423\u2013443 (2005)","journal-title":"Discrete Comput. Geom."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9070-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-008-9070-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9070-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T19:47:35Z","timestamp":1559072855000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-008-9070-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3,7]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,10]]}},"alternative-id":["9070"],"URL":"https:\/\/doi.org\/10.1007\/s00454-008-9070-1","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3,7]]}}}