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Betti number
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41	REFINED BOUNDS ON THE NUMBER OF CONNECTED COMPONENTS OF SIGN CONDITIONS ON A VARIETY SAL BARONE AND SAUGATA BASU Abstract. Let R be a real closed field, P, Q ⊂ R[X1 , . . . , Xk ] finite subsets of polynomials, with th Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-11-06 10:09:22 Algebraic geometry Commutative algebra Field extension Algebraic variety Algebraically closed field Zariski topology Betti number Puiseux series Algebraic closure Abstract algebra Algebra Field theory
42	COMPUTING THE BETTI NUMBERS OF SEMI-ALGEBRAIC SETS DEFINED BY PARTLY QUADRATIC SYSTEMS OF POLYNOMIALS SAUGATA BASU, DMITRII V. PASECHNIK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:26 Algebraic geometry Betti number Polynomial Semialgebraic set Ordinal number Probability theory Transcendental number Probability space Mathematics Abstract algebra Real algebraic geometry
43	Contemporary Mathematics Algorithmic Semi-algebraic Geometry and Topology – Recent Progress and Open Problems Saugata Basu Abstract. We give a survey of algorithms for computing topological invariants of semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:06 Real algebraic geometry Equations Algebraic geometry Semialgebraic set Algebraic variety Betti number Sheaf Algebraic topology Topology Abstract algebra Mathematics Algebra
44	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL 1. Brief Description Toda proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the cl Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:58 Field theory Algebraic geometry Polynomial Field extension Field Computational complexity theory Betti number Finite field Number Abstract algebra Mathematics Algebra
45	Computing the First Few Betti Numbers of Semi-algebraic Sets in Single Exponential Time Saugata Basu 1 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:07 Group theory Algebraic topology Mathematical structures Algebraic geometry Betti number Spectral sequence Singular homology Field Structure Algebra Abstract algebra Mathematics
46	´ COMPUTING THE EULER-POINCARE CHARACTERISTICS OF SIGN CONDITIONS Saugata Basu, Richard Pollack, and Marie-Franc Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:52 Algebraic topology Topological graph theory Algebraic geometry Euler characteristic Betti number Algebraic variety Field extension Simplicial complex Bernoulli number Abstract algebra Mathematics Topology
47	J. Eur. Math. Soc. 12, 529–553 c European Mathematical Society 2010 DOI[removed]JEMS/208 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:22 Field theory Algebraic topology Betti number Topological graph theory Polynomial Algebraic variety Field extension Field Puiseux series Abstract algebra Mathematics Algebra
48	spectral-vs-persistent9.pdf Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2013-10-06 09:48:49 Algebraic topology Spectral sequence Filtration Homological algebra Homology CW complex Linear map Sheaf Betti number Abstract algebra Topology Mathematics
49	Algebraic Topological Methods in Computer Science, II Department of Mathematics, University of Western Ontario Add to Reading List Source URL: www.math.uwo.ca Language: English - Date: 2004-07-12 10:31:31 Abstract algebra Manifold Directed algebraic topology Simplicial set CW complex Homotopy Simplicial homology Topological space Betti number Topology Mathematics Algebraic topology
50	Hypertrees and the 2 Betti numbers of the pure symmetric automorphism group Add to Reading List Source URL: www.math.ucsb.edu Language: English - Date: 2004-03-29 12:03:24 Mathematics Topological graph theory Cohomology Homological algebra Homology theory Betti number Covering space Abstract algebra Topology Algebraic topology

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