EMBEDDINGS INTO PRODUCTS AND SYMMETRIC PRODUCTS - AN ALGEBRAIC APPROACH

被引:0
|
作者
Koyama, Akira [1 ]
Krasinkiewicz, Jozef [2 ]
Spiez, Stanislaw [2 ]
机构
[1] Shizuoka Univ, Fac Sci, Dept Math, Shizuoka 4228529, Japan
[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
来源
HOUSTON JOURNAL OF MATHEMATICS | 2012年 / 38卷 / 02期
关键词
Embeddings; cohomology groups; products; symmetric products; METRIC-SPACES; MANIFOLDS; CURVES;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article we mostly study algebraic properties of n-dimensional "cyclic" compacta lying either in products of n curves or in the nth symmetric product of a curve. The basic results have been obtained for compacta admitting essential maps into the n-sphere S-n. One of the main results asserts that if a compactum X admits such a mapping and X embeds in a product of n curves then there exists an algebraically essential map X -> T-n into the n-torus; the same conclusion holds for X embeddable in the nth symmetric product of a curve. The existence of analgebraically essential mapping X -> T-n is equivalent to the existence of some elements a(1), . . . ,a(n) is an element of H-1 (X) whose cup product a(1)boolean OR . . . boolean OR a(n) is an element of H-n (X) is not zero, and implies that rank H-1(X) >= n and cat X > n. In particular, it follows that S-n, n >= 2, is not embeddable in the nth symmetric product of any curve. The case n = 2 answers in the negative a question of Illanes and Nadler.
引用
收藏
页码:611 / 641
页数:31
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