Seminar on Fiber Spaces

Thomas, Emery

doi:10.1007/bfb0097864

Cited by 58 publications

(35 citation statements)

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“…Motivated by this, in this section we study the number of stably equivalent smooth SO(3) bundles over ten dimensional CW-complex and when a stable bundle over a 11 dimensional complex has geometric dimension 3. The method to do this is to construct the Moore-Postnikov factorazition for the fibration Π : BSO(3) → BSO as far as we need and compute the indeterminacy of various obstructions along the line of Thomas [15].…”

Section: Appendix: Smooth S 2 -Bundles Over 10-complexmentioning

confidence: 99%

Topology of Dupin hypersurfaces with six distinct principal curvatures

Fang

1999

Math Z

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Let M be a Dupin hypersurface in the unit sphere S n+1 with six distinct principal curvatures. We will prove in the present paper that M is either diffeomorphic to SU (2) × SU (2)/Q 8 or homeomorphic to a tube around an embedded 5-dimensional complex Fermat hypersurface X 5 (2) in S 13 , where Q 8 ⊂ SU (2) = Sp(1) denotes the subgroup {±1, ±i, ±j, ±k} and X 5 (2) = {[z 0 , z 1 , · · · z 6 ] ∈ CP 6 |z 2 0 + z 2 1 + · · ·+ z 2 6 = 0}. Moreover, in the former case, all of the focal manifolds are diffeomorphic to S 3 × RP 2 ; In the latter case, one of the focal manifolds is homeomorphic to X 5 (2).

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Section: Appendix: Smooth S 2 -Bundles Over 10-complexmentioning

confidence: 99%

Topology of Dupin hypersurfaces with six distinct principal curvatures

Fang

1999

Math Z

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“…Remark. If n is odd, if B is one-connected, and if K(n, ri) -> E -> B is a fibration, which is not necessarily principal, then we can still deduce that p0(B)^ p0(E) p0(B)-k. The first inequality is clear, and the second inequality may be inferred by applying a spherical class resolution (Mahowald [10] or Thomas [14]) and using the Serre spectral sequence at each stage.…”

Section: An Upper Bound For Rk0(x)mentioning

confidence: 99%

On the rank of a space

Allday¹

1972

Trans. Amer. Math. Soc.

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Abstract. The rank of a space is defined as the dimension of the highest dimensional torus which can act almost-freely on the space. (By an almost-free action is meant one for which all the isotropy subgroups are finite.) This definition is shown to extend the classical definition of the rank of a Lie group. A conjecture giving an upper bound for the rank of a space in terms of its rational homotopy is investigated.

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“…Appendix. These Postnikov resolutions for the fiber map tt: Bm^> B are constructed by the techniques of [26]. We refer the reader also to [17] and [8] for the theory and construction of modified Postnikov resolutions.…”

Section: Sectionsmentioning

confidence: 99%

Some immersion theorems for projective spaces

Randall¹

1970

Trans. Amer. Math. Soc.

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Seminar on Fiber Spaces

Cited by 58 publications

References 0 publications

Topology of Dupin hypersurfaces with six distinct principal curvatures

Topology of Dupin hypersurfaces with six distinct principal curvatures

On the rank of a space

Some immersion theorems for projective spaces

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