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

Annales de l'institut Fourier (1982)

- Volume: 32, Issue: 4, page 205-219
- ISSN: 0373-0956

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topKumar, 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 -

## References

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- [4] E. FRIEDLANDER, P. A. GRIFFITHS and J. MORGAN, Homotopy theory and differential forms, Seminario di Geometria, (1972).
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- [6] B. KOSTANT, Lie group representations on polynomial rings, American journal of Mathematics, 85 (1963), 327-404. Zbl0124.26802MR28 #1252
- [7] D. SULLIVAN, Differential forms and the topology of Manifolds, Proceedings of the International Conference on Manifolds, Tokyo, (1973), 37-49. Zbl0319.58005MR51 #6838

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