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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.

Flat hierarchy

Vassily O. Manturov (2005)

Fundamenta Mathematicae

We consider the hierarchy flats, a combinatorial generalization of flat virtual links proposed by Louis Kauffman. An approach to constructing invariants for hierarchy flats is presented; several examples are given.

Flats in 3-manifolds

Michael Kapovich (2005)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Flensted-Jensen's functions attached to the Landau problem on the hyperbolic disc

Zouhaïr Mouayn (2007)

Applications of Mathematics

We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions Ψ μ , α on a concrete realization of the universal covering group of U ( 1 , 1 ) . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to μ , and corresponding to the eigenvalue 4 α ( α - 1 ) .

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