Rational self-equivalences of spaces in the genus of a product of quaternionic projective spaces
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- ISHIGURO Kenshi
- Fukuoka University
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- MØLLER Jesper
- Matematisk Institut, Universitesparken 5
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- NOTBOHM Dietrich
- Mathematisches Institut
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Abstract
For G=S3וs× S3, let X be a space such that the p-completion (X)p^ is homotopy equivalent to (BG)p^ for any prime p. We investigate the monoid of rational equivalences of X, denoted by ε0(X). This topological question is transformed into a matrix problem over Qotimes Z^, since ε0(BG) is the set of monomial matrices whose nonzero entries are odd squares. It will be shown that a submonoid of ε0(X), denoted by δ0(X), determines the decomposability of X. Namely, if Nodd denotes the monoid of odd natural numbers, Theorem 2 shows that the monoid δ0(X) is isomorphic to a direct sum of copies of Nodd. Moreover the space X splits into m indecomposable spaces if and only if δ0(X)_??_(Nodd)m. When such a space X is indecomposable, the relationship between [X, X] and [BG, BG] is discussed. Our results indicate that the homotopy set [X, X] contains less maps if X is not homotopy equivalent to the product of quaternionic projective spaces BG=HP∈ftyוs× HP∈fty.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 51 (1), 45-61, 1999
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390282680092799488
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- NII Article ID
- 10002151365
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- MRID
- 1661000
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- NDL BIB ID
- 4643257
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed