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Fixed points on torus fiber bundles over the circle

D. L. Gonçalves, D. Penteado, J. P. Vieira (2004)

Fundamenta Mathematicae

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S¹ for spaces which are fibrations over S¹ and the fiber is the torus ,T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S¹ to a fixed point free map. For the case where the fiber is a torus, we classify all maps over...

Generalized universal covering spaces and the shape group

Hanspeter Fischer, Andreas Zastrow (2007)

Fundamenta Mathematicae

If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception of evenly...

Generating varieties for the triple loop space of classical Lie groups

Yasuhiko Kamiyama (2003)

Fundamenta Mathematicae

For G = SU(n), Sp(n) or Spin(n), let C G ( S U ( 2 ) ) be the centralizer of a certain SU(2) in G. We have a natural map J : G / C G ( S U ( 2 ) ) → Ω ₀ ³ G . For a generator α of H ⁎ ( G / C G ( S U ( 2 ) ) ; ℤ / 2 ) , we describe J⁎(α). In particular, it is proved that J ⁎ : H ⁎ ( G / C G ( S U ( 2 ) ) ; ℤ / 2 ) → H ⁎ ( Ω ₀ ³ G ; ℤ / 2 ) is injective.

Currently displaying 221 – 240 of 689