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On the group of self-homotopy equivalence of a formal F0-space
Let X , Y be two formal F 0 -spaces. We show that any continuous map from X to Y is formal. Moreover, if [ X , Y ] denotes the set of homotopy classes from X to Y , E ( X ) the group of homotopy classes of self-homotopy equivalences of X and E ∗ ( X ) its subgroup of the elements inducing the iden...
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| Published in: | Bollettino della Unione matematica italiana (2008) 2023, Vol.16 (3), p.641-647 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | Let
X
,
Y
be two formal
F
0
-spaces. We show that any continuous map from
X
to
Y
is formal. Moreover, if [
X
,
Y
] denotes the set of homotopy classes from
X
to
Y
,
E
(
X
)
the group of homotopy classes of self-homotopy equivalences of
X
and
E
∗
(
X
)
its subgroup of the elements inducing the identity on
H
∗
(
X
)
, then
[
X
,
Y
]
=
Hom
(
H
∗
(
Y
)
,
H
∗
(
X
)
)
,
E
(
X
)
≅
aut
(
H
∗
(
X
)
)
and
E
∗
(
X
)
is trivial. |
|---|---|
| ISSN: | 1972-6724 2198-2759 |
| DOI: | 10.1007/s40574-023-00354-y |