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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.

Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

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