The Milnor–Stasheff Filtration on Spaces and Generalized Cyclic Maps
The Milnor–Stasheff Filtration on Spaces and Generalized Cyclic Maps
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空间和广义循环映射上的 Milnor-Stasheff 过滤
DOI：
10.4153/cmb-2011-130-8
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Y. Yoon
中科院分区：
文献类型：
--
作者：
Norio Iwase;M. Mimura;Nobuyuki Oda;Y. Yoon
Abstract The concept of ${{C}_{k}}$ -spaces is introduced, situated at an intermediate stage between $H$ -spaces and $T$ -spaces. The ${{C}_{k}}$ -space corresponds to the $k$ -th Milnor–Stasheff filtration on spaces. It is proved that a space $X$ is a ${{C}_{k}}$ -space if and only if the Gottlieb set $G(Z,\,X)\,=\,[Z,\,X]$ for any space $Z$ with cat $Z\,\le \,k$ , which generalizes the fact that $X$ is a $T$ -space if and only if $G(\sum B,\,X)\,=\,[\sum B,\,X]$ for any space $B$ . Some results on the ${{C}_{k}}$ -space are generalized to the $C_{k}^{f}$ -space for a map $f\,:\,A\,\to \,X$ . Projective spaces, lens spaces and spaces with a few cells are studied as examples of ${{C}_{k}}$ -spaces, and non- ${{C}_{k}}$ -spaces.
Abstract The concept of ${{C}_{k}}$ -spaces is introduced, situated at an intermediate stage between $H$ -spaces and $T$ -spaces. The ${{C}_{k}}$ -space corresponds to the $k$ -th Milnor–Stasheff filtration on spaces. It is proved that a space $X$ is a ${{C}_{k}}$ -space if and only if the Gottlieb set $G(Z,\,X)\,=\,[Z,\,X]$ for any space $Z$ with cat $Z\,\le \,k$ , which generalizes the fact that $X$ is a $T$ -space if and only if $G(\sum B,\,X)\,=\,[\sum B,\,X]$ for any space $B$ . Some results on the ${{C}_{k}}$ -space are generalized to the $C_{k}^{f}$ -space for a map $f\,:\,A\,\to \,X$ . Projective spaces, lens spaces and spaces with a few cells are studied as examples of ${{C}_{k}}$ -spaces, and non- ${{C}_{k}}$ -spaces.
Ganea 猜想和 Lusternik-Schnirelmann 范畴的最新进展
DOI：
--
发表时间：
2004
期刊：
Sugaku 56
影响因子：
--
作者：
Norio Iwase;Donald Stanley;Jeffrey Strom;Norio Iwase
通讯作者：
Norio Iwase
拆分同伦类型中的有理部分
DOI：
--
发表时间：
2005
期刊：
Topology Appl. 153
影响因子：
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作者：
N.Iwase;N.Oda
通讯作者：
N.Oda