منابع مشابه
Homotopical Nilpotence of S3
In [l] Berstein and Ganea define the nilpotence of an ü-space to be the least integer » such that the »-commutator is nullhomotopic. We prove that S3 with the usual multiplication is 4 nilpotent. Let X be an ii-space. The 2-commutator c2: XXX—>X is defined by c2(x, y) =xyx~1y~1 where the multiplication and inverses are given by the ü-space structure of X. The »-commutator cn: X"-+X is defined i...
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We give a new approach to intersection theory. Our “cycles” are closed manifolds mapping into compact manifolds and our “intersections” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [H-Q], but our proofs are fundamentally di...
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Consider two k-gons P and Q. We say that the billiard flows in P and Q are homotopically equivalent if the set of conjugacy classes in the fundamental group of P which contain a periodic billiard orbit agrees with the analogous set for Q. We study this equivalence relationship and compare it to the equivalence relations, order equivalence and code equivalence, introduced in [BT1, BT2]. In parti...
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If G is a connected compact Lie group, then for almost all prime numbers p the mod p cohomology ring of the classifying space BG is a finitely generated polynomial algebra. In 1961, N. Steenrod [24] asked in general for a determination of all spaces X such that H∗(X,Fp) is a finitely generated polynomial algebra (i.e., such that X has a polynomial cohomology ring); at that time, the only exampl...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1964
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1964-0169244-9