Hyperplane skew resolutions and their applications
نویسندگان
چکیده
منابع مشابه
Hyperplane Arrangements and Linear Strands in Resolutions
The cohomology ring of the complement of a central complex hyperplane arrangement is the well-studied Orlik-Solomon algebra. The homotopy group of the complement is interesting, complicated, and few results are known about it. We study the ranks for the lower central series of such a homotopy group via the linear strand of the minimal free resolution of the field C over the Orlik-Solomon algebra.
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If M is the complement of a hyperplane arrangement, and A = H(M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dimTor A i (k, k)i, of the linear strand in a minimal free resolution of k over A. We use the Cartan-Eilenberg change of rings spectral sequence to relate...
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In [2], a connection was made between the characteristic-free resolution of the three-rowed partition, (2, 2, 2), and its characteristic-zero resolution described by A. Lascoux. The method used there was to take the known general resolution, modify the boundary map exploiting the fact that we can divide when we’re over the rationals, and then reduce the large general resolution to the much slim...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1988
ISSN: 0097-3165
DOI: 10.1016/0097-3165(88)90047-7