On the Multiple Points of the Self-Transverse Immersions of the Real Projective Space and the Milnor Manifold

Kamata, Masayoshi; Ono, Kiyonobu

doi:10.2206/kyushujm.60.331

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Milnor Manifolds1

It Is Known Due To Conner and Floyd1

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Cited by 2 publications

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“…These manifolds have been well studied in the past. See [11,15,29] for some recent results. Their cohomology algebra is also well known [5,18], and we need it for the proofs of our main results.…”

Section: Milnor Manifoldsmentioning

confidence: 99%

Free Actions of Some Compact Groups on Milnor Manifolds

Dey

Singh

2018

Glasgow Math. J.

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In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ℤ2 and $\mathbb{S}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk–Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to the Euclidean plane.

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Section: Milnor Manifoldsmentioning

confidence: 99%

Free Actions of Some Compact Groups on Milnor Manifolds

Dey

Singh

2018

Glasgow Math. J.

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show abstract

“…These manifolds have been well studied in the past. See for example [17,21,26] for recent results. Their cohomology algebra is also well known, and we will use it in the proofs of our main theorems.…”

Section: It Is Known Due To Conner and Floydmentioning

confidence: 99%

Free 2-rank of symmetry of products of Milnor manifolds

Singh

2014

Homology, Homotopy and Applications

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Abstract. A real Milnor manifold is the non-singular hypersurface of degree (1, 1) in the product of two real projective spaces. These manifolds were introduced by Milnor to give generators for the unoriented cobordism algebra, and they admit free actions by elementary abelian 2-groups. In this paper, we obtain some results on the free 2-rank of symmetry of products of finitely many real Milnor manifolds under the assumption that the induced action on mod 2 cohomology is trivial. Similar results are obtained for complex Milnor manifolds which are defined analogously. Here the free 2-rank of symmetry of a topological space is the maximal rank of an elementary abelian 2-group which acts freely on that space.

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On the Multiple Points of the Self-Transverse Immersions of the Real Projective Space and the Milnor Manifold

Abstract: Abstract.We study the Euler characteristic modulo 2 of the manifold immersed in the multiple point set of the self-transverse immersions of the real projective space RP n and the Milnor manifold H m,n in the sphere.

Cited by 2 publications

References 11 publications

Free Actions of Some Compact Groups on Milnor Manifolds

Free Actions of Some Compact Groups on Milnor Manifolds

Free 2-rank of symmetry of products of Milnor manifolds

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