On a type of subgroups of a compact Lie group
Open accessAbstract
Let G be a connected compact Lie group and H a connected closed subgroup. Then H is an orientable submanifold of G and we may consider H as a cycle in G. In his interesting paper on the topology of group manifolds H. Samelson has proved that, if H is not homologous to 0, then the homology ring of the coset space G/H is isomorphic to the homology ring of a product space of odd dimensional spheres and the homology ring of G is isomorphic to that of the product of the spaces H and G/H. On the other hand, in a recent investigation of fibre bundles’ T. Kudo has shown that, if the homology ring of the coset space G/H is isomorphic to that of an odd dimensional sphere, then H is not homologous to 0.
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Samelson, H. (1952) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1952-09544-6 · Cited by 219 · see citing works
Homogeneous Sphere Bundles and the Isotropic Riemann Manifolds
Nagano, T. (1959) · Nagoya Mathematical Journal · doi:10.1017/s0027763000006668 · Cited by 30 · see citing works
On Homogeneous Cohomology Spheres
Bredon, G. E. (1961) · Annals of Mathematics · doi:10.2307/1970317 · Cited by 19 · see citing works
Compact transformation groups on $Z\sb2$-cohomology spheres with orbit of codimension 1
Asoh, T. (1981) · Hiroshima Mathematical Journal · doi:10.32917/hmj/1206133992 · Cited by 14 · see citing works
Actions of compact connected Lie groups on simply connected rational cohomology $5$-spheres
Mukōyama, K. (1989) · Tohoku Mathematical Journal · doi:10.2748/tmj/1178227870 · Cited by 1 · see citing works
Table of Publications. Vol. 1–Vol. 16
(1960) · Nagoya Mathematical Journal · doi:10.1017/s0027763000027227 · Cited by 1 · see citing works
Equivariant formality of corank-one isotropy actions and products of rational spheres
Carlson, J. D., & He, C. (2023) · Mathematische Zeitschrift · doi:10.1007/s00209-023-03319-1
- Authors
- Matsushima, Y.
- Affiliations
- Nagoya University (JP)
- Corresponding author
- Matsushima, Yozô
- Venue
- Nagoya Mathematical Journal
- Publisher
- Cambridge University Press (CUP)
- Published
- 1951-02
- Volume
- 2
- Pages
- 1-15
- ISSN
- 0027-7630 (ISSN-L)
- 2152-6842
- OpenAlex
- W1604778870
- Semantic Scholar
- 3cabfba6241a162ffc23f13411e96c09dfafffde
- Cited by
- 7
- References
- 0
- Citations by year
- 2023: 1
- FWCI
- 0.72
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Nagoya Mathematical Journal (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Algebra and Geometry
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- compact Lie groups, closed subgroups, coset spaces, homology classes, fiber bundles, odd-dimensional spheres, Kudos
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