Abstract
For a map $$f:X\rightarrow Y$$
f
:
X
→
Y
, there is the relative model $$M(Y)=(\Lambda V,d)\rightarrow (\Lambda V\otimes \Lambda W,D)\simeq M(X)$$
M
(
Y
)
=
(
Λ
V
,
d
)
→
(
Λ
V
⊗
Λ
W
,
D
)
≃
M
(
X
)
by Sullivan model theory (Félix et al., Rational homotopy theory, graduate texts in mathematics, Springer, Berlin, 2007). Let $$\mathrm{Baut}_1X$$
Baut
1
X
be the Dold–Lashof classifying space of orientable fibrations with fiber X (Dold and Lashof, Ill J Math 3:285–305, 1959]). Its DGL (differential graded Lie algebra)-model is given by the derivations $$\mathrm{Der}M(X)$$
Der
M
(
X
)
of the Sullivan minimal model M(X) of X. Then we consider the condition that the restriction $$b_f:\mathrm{Der} (\Lambda V\otimes \Lambda W,D)\rightarrow \mathrm{Der}(\Lambda V,d) $$
b
f
:
Der
(
Λ
V
⊗
Λ
W
,
D
)
→
Der
(
Λ
V
,
d
)
is a DGL-map and the related topics.
On rational homotopy and minimal models
