scholarly journals Natural duality, modality, and coalgebra

2012 ◽  
Vol 216 (3) ◽  
pp. 565-580 ◽  
Author(s):  
Yoshihiro Maruyama
Keyword(s):  
Natural Duality

scholarly journals Graphs, Links, and Duality on Surfaces

2010 ◽  
Vol 20 (2) ◽  
pp. 267-287 ◽  
Author(s):  
VYACHESLAV KRUSHKAL
Keyword(s):  
Planar Graphs ◽  
Jones Polynomial ◽  
Tutte Polynomial ◽  
Natural Duality ◽  
Polynomial Invariant ◽  
Topological Duality ◽  
Ribbon Graphs ◽  
Virtual Links ◽  
Graphs On Surfaces ◽  
Tutte Polynomials

We introduce a polynomial invariant of graphs on surfaces,PG, generalizing the classical Tutte polynomial. Topological duality on surfaces gives rise to a natural duality result forPG, analogous to the duality for the Tutte polynomial of planar graphs. This property is important from the perspective of statistical mechanics, where the Tutte polynomial is known as the partition function of the Potts model. For ribbon graphs,PGspecializes to the well-known Bollobás–Riordan polynomial, and in fact the two polynomials carry equivalent information in this context. Duality is also established for a multivariate version of the polynomialPG. We then consider a 2-variable version of the Jones polynomial for links in thickened surfaces, taking into account homological information on the surface. An analogue of Thistlethwaite's theorem is established for these generalized Jones and Tutte polynomials for virtual links.

On a Natural Duality Between Grothendieck Categories

2008 ◽  
Vol 36 (6) ◽  
pp. 2079-2091 ◽  
Author(s):  
F. Castaño-iglesias
Keyword(s):  
Natural Duality

The Strong ϕ Topology on Symmetric Sequence Spaces

1985 ◽  
Vol 37 (6) ◽  
pp. 1112-1133
Author(s):  
William H. Ruckle
Keyword(s):  
Finite Number ◽  
Linear Space ◽  
Natural Duality ◽  
Sequence Spaces ◽  
Image Position

The strong ϕ topology. Let S be a linear space of real sequences written in functional notationThere is a natural duality between S and the space ϕ of sequences which are eventually ϕ given by the equationThe series has only a finite number of nonzero terms since t is in ϕ.A subset B of ϕ is called S-bounded iffor each s in S.

scholarly journals Natural dualities for dihedral varieties

1996 ◽  
Vol 61 (2) ◽  
pp. 216-228 ◽  
Author(s):  
B. A. Davey ◽  
R. W. Quackenbush
Keyword(s):  
Abelian Variety ◽  
Natural Duality ◽  
Variety Of Groups

AbstractA strong, natural duality is established for the variety by a dihedral gruop of order 2m with m odd. This is the first natural duality for a non-abelian variety of groups.

THE LATTICE OF ALTER EGOS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250007 ◽  
Author(s):  
BRIAN A. DAVEY ◽  
JANE G. PITKETHLY ◽  
ROSS WILLARD
Keyword(s):  
Duality Theory ◽  
Finite Algebra ◽  
Galois Connection ◽  
Natural Duality ◽  
Algebraic Lattice ◽  
Finite Set ◽  
Partial Algebras ◽  
Quasi Order ◽  
Basic Concepts

We introduce a new Galois connection for partial operations on a finite set, which induces a natural quasi-order on the collection of all partial algebras on this set. The quasi-order is compatible with the basic concepts of natural duality theory, and we use it to turn the set of all alter egos of a given finite algebra into a doubly algebraic lattice. The Galois connection provides a framework for us to develop further the theory of natural dualities for partial algebras. The development unifies several fundamental concepts from duality theory and reveals a new understanding of full dualities, particularly at the finite level.

scholarly journals Nondualisable semigroups

2002 ◽  
Vol 65 (3) ◽  
pp. 491-502 ◽  
Author(s):  
David Hobby
Keyword(s):  
Infinite Family ◽  
Natural Duality ◽  
Finite Semigroups

An infinite family of finite semigroups is studied. It is shown that most of them do not generate a quasivariety which admits a natural duality.

scholarly journals p-topological andp-regular: dual notions in convergence theory

1999 ◽  
Vol 22 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Scott A. Wilde ◽  
D. C. Kent
Keyword(s):  
Natural Duality ◽  
Convergence Theory ◽  
Convergence Criteria ◽  
Convergence Space ◽  
Regular Convergence ◽  
Convergence Spaces ◽  
Simple Characterization ◽  
Topological Convergence

The natural duality between “topological” and “regular,” both considered as convergence space properties, extends naturally top-regular convergence spaces, resulting in the new concept of ap-topological convergence space. Taking advantage of this duality, the behavior ofp-topological andp-regular convergence spaces is explored, with particular emphasis on the former, since they have not been previously studied. Their study leads to the new notion of a neighborhood operator for filters, which in turn leads to an especially simple characterization of a topology in terms of convergence criteria. Applications include the topological and regularity series of a convergence space.

scholarly journals The algebra of cell-zeta values

2010 ◽  
Vol 146 (3) ◽  
pp. 731-771 ◽  
Author(s):  
Francis Brown ◽  
Sarah Carr ◽  
Leila Schneps
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Cohomology Group ◽  
Differential Forms ◽  
Natural Duality ◽  
Connected Component ◽  
Real Numbers ◽  
Zeta Values ◽  
Definition Of ◽  
Formal Version

AbstractIn this paper, we introduce cell-forms on 𝔐0,n, which are top-dimensional differential forms diverging along the boundary of exactly one cell (connected component) of the real moduli space 𝔐0,n(ℝ). We show that the cell-forms generate the top-dimensional cohomology group of 𝔐0,n, so that there is a natural duality between cells and cell-forms. In the heart of the paper, we determine an explicit basis for the subspace of differential forms which converge along a given cell X. The elements of this basis are called insertion forms; their integrals over X are real numbers, called cell-zeta values, which generate a ℚ-algebra called the cell-zeta algebra. By a result of F. Brown, the cell-zeta algebra is equal to the algebra of multizeta values. The cell-zeta values satisfy a family of simple quadratic relations coming from the geometry of moduli spaces, which leads to a natural definition of a formal version of the cell-zeta algebra, conjecturally isomorphic to the formal multizeta algebra defined by the much-studied double shuffle relations.

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