Equivariant betti numbers for symmetric varieties
نویسندگان
چکیده
منابع مشابه
Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
Let R be a real closed field. The problem of obtaining tight bounds on the Betti numbers of semi-algebraic subsets of R in terms of the number and degrees of the defining polynomials has been an important problem in real algebraic geometry with the first results due to Olĕınik and Petrovskĭı, Thom and Milnor. These bounds are all exponential in the number of variables k. Motivated by several ap...
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Let R be a real closed field. We prove that for any fixed d, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of Rk defined by polynomials of degrees bounded by d vanishes in dimensions d and larger. This vanishing result is tight. Using a new geometric approach we also prove an upper bound of dO(d)sdkbd/2c−1 on the equivariant Betti numbers of closed symmet...
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The regular Z-covers of a finite cell complex X are parameterized by the Grassmannian of r-planes in H(X,Q). Moving about this variety, and recording when the Betti numbers b1, . . . , bi of the corresponding covers are finite carves out certain subsets Ωr(X) of the Grassmannian. We present here a method, essentially going back to Dwyer and Fried, for computing these sets in terms of the jump l...
متن کاملBounding the equivariant Betti numbers and computing the generalized Euler-Poincaré characteristic of symmetric semi-algebraic sets
Unlike the well known classical bounds due to Oleinik and Petrovskii, Thom and Milnor on the Betti numbers of (possibly non-symmetric) real algebraic varieties and semialgebraic sets, the above bound is polynomial in k when the degrees of the defining polynomials are bounded by a constant. Moreover, our bounds are asymptotically tight. As an application we improve the best known bound on the Be...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90180-t