scholarly journals Rational cohomologies of classifying spaces for homogeneous spaces of small rank

2016 ◽  
Vol 5 (4) ◽  
pp. 225-237
Author(s):  
Hirokazu Nishinobu ◽  
Toshihiro Yamaguchi
Keyword(s):  
Homogeneous Spaces ◽  
Classifying Spaces ◽  
Small Rank

scholarly journals Sullivan minimal models of classifying spaces for non-formal spaces of small rank

2015 ◽  
Vol 196 ◽  
pp. 290-307 ◽  
Author(s):  
Hirokazu Nishinobu ◽  
Toshihiro Yamaguchi
Keyword(s):  
Classifying Spaces ◽  
Minimal Models ◽  
Small Rank

Maximal Homotopy Lie Subgroups of Maximal Rank

1988 ◽  
Vol 40 (04) ◽  
pp. 769-787 ◽  
Author(s):  
John A. Frohliger
Keyword(s):  
Lie Group ◽  
Homogeneous Spaces ◽  
Maximal Rank ◽  
Homotopy Equivalent ◽  
Classifying Spaces ◽  
Loop Spaces ◽  
Connected Subgroup ◽  
Image Position ◽  
Lie Subgroup ◽  
Connected Lie Group

Let G be a compact connected Lie group with H a connected subgroup of maximal rank. Suppose there exists a compact connected Lie subgroup K with H ⊂ K ⊂ G. Then there exists a smooth fiber bundle G/H → G/K with K/H as the fiber. (See for example [13].) This can be incorporated into a diagram involving the classifying spaces as follows: (1) Here π, ϕ, ϕ 1 and ϕ 2 denote fibrations. We also know that the homogeneous spaces and the Lie groups, which are homotopy equivalent to the loop spaces of their respective classifying spaces, are homotopy equivalent to connected finite complexes. Now suppose H is a maximal subgroup. Can there still exist spaces, which we will call BK, K/H, and G/K, and fibrations so that diagram (1) is still valid? This paper will show that in many cases either G/K or K/H will be homo topically trivial.

Application of Morse theory to some homogeneous spaces

1969 ◽  
Vol 21 (3) ◽  
pp. 343-353 ◽  
Author(s):  
S. Ramanujan
Keyword(s):  
Morse Theory ◽  
Homogeneous Spaces

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

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