A $G$-minimal model for principal $G$-bundles

Kumar, Shrawan. "A $G$-minimal model for principal $G$-bundles." Annales de l'institut Fourier 32.4 (1982): 205-219. <http://eudml.org/doc/74561>.

@article{Kumar1982,
abstract = {Sullivan associated a uniquely determined $DGA\big |_\{\bf Q\}$ to any simply connected simplicial complex $E$. This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space $E$. In case $E$ is the total space of a principal $G$-bundle, ($G$ is a compact connected Lie-group) we associate a $G$-equivariant model $U_G[E]$, which is a collection of “$G$-homotopic” $DGA$’s$\big |_\{\bf R\}$ with $G$-action. $U_G[E]$ will, in general, be different from the Sullivan’s minimal model of the space $E$. $U_G[E]$ contains the total rational homotopy information of the spaces $E$, $E/G$ and, in addition, it incorporates the action of $G$ (on $E$).},
author = {Kumar, Shrawan},
journal = {Annales de l'institut Fourier},
keywords = {total space of a principal G-bundle; compact connected Lie-group; G-equivariant minimal models; equivariant rational homotopy theory},
language = {eng},
number = {4},
pages = {205-219},
publisher = {Association des Annales de l'Institut Fourier},
title = {A $G$-minimal model for principal $G$-bundles},
url = {http://eudml.org/doc/74561},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Kumar, Shrawan
TI - A $G$-minimal model for principal $G$-bundles
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 4
SP - 205
EP - 219
AB - Sullivan associated a uniquely determined $DGA\big |_{\bf Q}$ to any simply connected simplicial complex $E$. This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space $E$. In case $E$ is the total space of a principal $G$-bundle, ($G$ is a compact connected Lie-group) we associate a $G$-equivariant model $U_G[E]$, which is a collection of “$G$-homotopic” $DGA$’s$\big |_{\bf R}$ with $G$-action. $U_G[E]$ will, in general, be different from the Sullivan’s minimal model of the space $E$. $U_G[E]$ contains the total rational homotopy information of the spaces $E$, $E/G$ and, in addition, it incorporates the action of $G$ (on $E$).
LA - eng
KW - total space of a principal G-bundle; compact connected Lie-group; G-equivariant minimal models; equivariant rational homotopy theory
UR - http://eudml.org/doc/74561
ER -