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Fibred closed braids with disc-band fibre surfaces

Marta Rampichini (2004)

Bollettino dell'Unione Matematica Italiana

A classical result by Stallings provides a necessary and sufficient condition to decide whether a given embedded surface S is a fibre in S 3 - ∂ ⁡ S . In this paper it is described how to find a candidate fibre surface for a a link presented as a closed braid. Also it is described an implemented algorithm to find the main ingredients of the necessary and sufficient condition of Stallings, namely presentations of the fundamental groups of the surface and of its complement in S 3 , and an explicit expression of...

Fibring the complement of the Fenn-Rolfsen link.

Roger Fenn (1989)

Publicacions Matemàtiques

In this note it is shown that the complement of the singular linked spheres in four dimensions defined by Fenn and Rolfsen can be fibred by tori.Also a symmetry between the two components is revealed which shows that the image provides an example of a Spanier-Whitehead duality. This provides an immediate proof that the α-invariant is non zero.

Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

We describe the finite group actions, up to equivalence, which can act on the orbifold Σ ( 2 , 2 , 2 ) , and their quotient types. This is then used to consider actions on prism manifolds M ( b , d ) which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If ϕ : G → Homeo ( M ( b , d ) ) is such an action, we show that M ( b , d ) = M ( b , 2 ) and M ( b , 2 ) / ϕ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by Σ ( 2 , 2 , 2 ) . For the standard actions, we compute the fundamental group of M ( b , 2 ) / ϕ and indicate when...

Finite group actions on 2- dimensional CW-complexes

Dorabiala, Wojciech (1994)

Proceedings of the Winter School "Geometry and Physics"

Let X be a cell complex obtained by attaching a 2-cell to a finite bouquet of circles (for example, a closed surface). In terms of the combinatorial type of the attaching map, the paper gives conditions for the existence of a fixed point free (topological) homeomorphism of the complex X . Also, quotients of finite group actions on such complexes are considered as well as a condition under which the induced actions on cohomology are trivial.

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