PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES

Title & Authors
PRINCIPAL FIBRATIONS AND GENERALIZED H-SPACES
Yoon, Yeon Soo;

Abstract
For a map $\small{f:A{\rightarrow}X}$, there are concepts of $\small{H^f}$-spaces, $\small{T^f}$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $\small{H^f}$-space, any $\small{H^f}$-space is a $\small{T^f}$-space. For a principal fibration $\small{E_k{\rightarrow}X}$ induced by $\small{k:X{\rightarrow}X^{\prime}}$ from $\small{{\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}}$, we obtain some sufficient conditions to having liftings $\small{H^{\bar{f}}}$-structures and $\small{T^{\bar{f}}}$-structures on $\small{E_k}$ of $\small{H^f}$-structures and $\small{T^f}$-structures on X respectively. We can also obtain some results about $\small{H^f}$-spaces and $\small{T^f}$-spaces in Postnikov systems for spaces, which are generalizations of Kahn`s result about H-spaces.
Keywords
$\small{H^f}$-spaces;$\small{T^f}$-spaces for maps;Postnikov systems;
Language
English
Cited by
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