Topological Duality and Algebraic Completions

2021 ◽  
pp. 143-184
Author(s):  
Mai Gehrke
Keyword(s):  
Topological 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.

TOPOLOGICAL DUALITY BETWEEN REAL SCALAR AND SPINOR FIELDS IN QUANTUM FIELD THEORY, COSMOLOGY, QUANTUM THEORIES OF FUNDAMENTAL EXTENDED OBJECTS

1994 ◽  
Vol 09 (01) ◽  
pp. 1-37 ◽  
Author(s):  
YU. P. GONCHAROV
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Theories ◽  
Topological Duality ◽  
Real Scalar ◽  
Spinor Fields ◽  
The Given ◽  
Kaluza Klein

This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.

scholarly journals A topological duality for mildly distributive meet-semilattices

2018 ◽  
pp. 265-284 ◽  
Author(s):  
Sergio A. Celani ◽  
Luciano J. González
Keyword(s):  
Topological Duality

scholarly journals Lattices whose ideal lattice is Stone

1983 ◽  
Vol 26 (1) ◽  
pp. 107-112 ◽  
Author(s):  
R. Beazer
Keyword(s):  
Distributive Lattice ◽  
Dual Space ◽  
Sufficient Conditions ◽  
Distributive Lattices ◽  
Stone Algebra ◽  
Ideal Lattice ◽  
Topological Duality ◽  
Bounded Distributive Lattice ◽  
Image Position ◽  
The Ideal

An elementary fact about ideal lattices of bounded distributive lattices is that they belong to the equational class ℬω of all distributive p-algebras (distributive lattices with pseudocomplementation). The lattice of equational subclasses of ℬω is known to be a chainof type (ω+l, where ℬ0 is the class of Boolean algebras and ℬ1 is the class of Stone algebras. G. Grätzer in his book [7] asks after a characterisation of those bounded distributive lattices whose ideal lattice belongs to ℬ (n≧1). The answer to the problem for the case n = 0 is well known: the ideal lattice of a bounded lattice L is Boolean if and only if L is a finite Boolean algebra. D. Thomas [10] recently solved the problem for the case n = 1 utilising the order-topological duality theory for bounded distributive lattices and in [5] W. Bowen obtained another proof of Thomas's result via a construction of the dual space of the ideal lattice of a bounded distributive lattice from its dual space. In this paper we give a short, purely algebraic proof of Thomas's result and deduce from it necessary and sufficient conditions for the ideal lattice of a bounded distributive lattice to be a relative Stone algebra.

A topological duality for strong Boolean posets

2019 ◽  
Vol 69 (3) ◽  
pp. 497-506
Author(s):  
Zhenzhu Yuan ◽  
Qingguo Li
Keyword(s):  
Topological Representation ◽  
Topological Duality ◽  
New Class ◽  
Boolean Lattices

Abstract In this paper, we define a new class of posets which are complemented and ideal-distributive, we call these posets strong Boolean. This definition is a generalization of Boolean lattices on posets, and is different from Boolean posets. We give a topology on the set of all prime Frink ideals in order to obtain the Stone’s topological representation for strong Boolean posets. A discussion of a duality between the categories of strong Boolean posets and BP-spaces is also presented.

A topological duality for tense $\boldsymbol{LM_n}$-algebras and applications1

2018 ◽  
Vol 26 (4) ◽  
pp. 339-380 ◽  
Author(s):  
Aldo V Figallo ◽  
Inés Pascual ◽  
Gustavo Pelaitay
Keyword(s):  
Topological Duality
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