منابع مشابه
Tori and essential dimension
The present paper deals with algebraic tori and essential dimension but in three unrelated contexts. After a recollection on essential dimension and generic torsors we explicitly construct a generic torsor for PGLn, n ≥ 5 odd. We also discuss the so called “tori method” which gives a geometric proof of a result of Ledet on the essential dimension of a cyclic group (see [4, 5]). In the last sect...
متن کاملEssential Dimension of Algebraic Tori
The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broad class of groups, which includes all algebraic tori.
متن کاملKnot Adjacency, Genus and Essential Tori
A knot K is called n-adjacent to another knot K , if K admits a projection containing n “generalized crossings” such that changing any 0 < m ≤ n of them yields a projection of K . We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer the question of the extent to which non-isotopic knots can be adjacent to each o...
متن کاملESSENTIAL p-DIMENSION OF ALGEBRAIC TORI
The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broader class of groups, which includes all algebraic tori.
متن کاملWhen Incompressible Tori Meet Essential Laminations
Roussarie and Thurston [Ro], [Th] showed that given a taut foliation F and an incompressible torus T in a 3-manifold M , the torus may be isotoped so that it is either transverse to the leaves of the foliation, or is equal to one of the leaves of the foliation. This result was known to be false in the more general context of a foliation F without Reeb components. The only obstruction, however [...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2006
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm189-3-1