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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 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.

Homomorphic extensions of Johnson homomorphisms via Fox calculus

Bernard Perron (2004)

Annales de l’institut Fourier

Using Fox differential calculus, for any positive integer k , we construct a map on the mapping class group ℳ g , 1 of a surface of genus g with one boundary component, such that, when restricted to an appropriate subgroup, it coincides with the k + 1 t h Johnson-Morita homomorphism. This allows us to construct very easily a homomorphic extension to ℳ g , 1 of the second and third Johnson-Morita homomorphisms.

Homotopy classification of nanophrases with at most four letters

Tomonori Fukunaga (2011)

Fundamenta Mathematicae

We give a homotopy classification of nanophrases with at most four letters. It is an extension of the classification of nanophrases of length 2 with at most four letters, given by the author in a previous paper. As a corollary, we give a stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components.

Mapping class group and the Casson invariant

Bernard Perron (2004)

Annales de l’institut Fourier

Using a new definition of the second and third Johsnon homomorphisms, we simplify and extend the work of Morita on the Casson invariant of homology-spheres defined by Heegard splittings. In particular, we calculate the Casson invariant of the homology-sphere obtained by gluing two handlebodies along a homeomorphism of the boundary belonging to the Torelli subgroup.

Minimal degree sequence for 2-bridge knots

Prabhakar Madeti, Rama Mishra (2006)

Fundamenta Mathematicae

We discuss polynomial representations for 2-bridge knots and determine the minimal degree sequence for all such knots. We apply the connection between rational tangles and 2-bridge knots.

Currently displaying 21 – 40 of 93