Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp
Authors.
myself
Thesis.
Master Thesis, Kyushu University, 1983
Abstract.
H-space (Hopf space) is a topological space with a multiplication like a Lie group. However, an H-space is not required to have a strict unit but a homotopy unit, nor to satisfy the associativity condition.
Such H spaces are studied first by H. Hopf [6] followed by A. Borel [2], W. Browder [3] and many others and are known to have a similar properties to Lie groups in the homotopy-theoretical view point.
Generally, an associative H-space is associated with "projective spaces" and the classifying space as their inductive limit, and, even just an H-space is associated with "projective plane".
Moreover we know that there are infinitely many steps between just an H-space and an associative H-space, using the idea of 'an H-space with an An-structure' (J. Stasheff [15,16], A. Zabrodsky [20]), which is actually associated with "projective space of at most n-th stage".
However in [16], a (homotopy-theoretical) characterization of a map preserving An structures is 'extremely complicated' and the arguments are restricted to a map with an associative target.
While we treat, in the present paper, such a map only in our applications, we give the characterization in full generality for future use.
(snip)
- On the ring structure of K*(XPn) (adobe-pdf file, 591KB)