紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2019, 56(1), p. 75-90

ON GENERALIZED DOLD MANIFOLDS

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2019-01

Let X be a smooth manifold with a (smooth) involution σ : X → X such that Fix(σ) ≠ ∅. We call the space P(m, X) := Sm × X/ ～ where (v, x) ～ (−v,σ(x)) a generalized Dold manifold. When X is an almost complex manifold and the differential Tσ : TX → TX is conjugate complex linear on each fibre, we obtain a formula for the Stiefel-Whitney polynomial of P(m, X) when H¹(X; ℤ₂) = 0. We obtain results on stable parallelizability of P(m, X) and a very general criterion for the (non) vanishing of the unoriented cobordism class [P(m, X)] in terms of the corresponding properties for X. These results are applied to the case when X is a complex flag manifold.

10.18910/71136

71136

ON GENERALIZED DOLD MANIFOLDS

Osaka University and Osaka City University, Departments of Mathematics

英語

2019-01

Osaka Journal of Mathematics

56

1

75

90

https://hdl.handle.net/11094/71136

10.18910/71136

https://doi.org/10.18910/71136