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Duality in Toric Topology
We characterise integral Poincaré duality moment-angle complexes...
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Duality theorems in topology
The present chapter is devoted to the early work on duality phenomena in topology. Of course, topology is a field which emerged from geometry during...
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Duality à la Bourbaki
In this chapter, we will investigate an aspect in the post-1930 history of duality which deserves special attention, namely the influence of...
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The historical development of Pontrjagin duality
This chapter has several aims. The first aim is a historical description of two parts of Lev Pontrjagin’s scientific work, namely his work on...
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On the distribution of Alexander polynomials in certain families of closed braids
We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links...
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Philosophical and mathematical duality in Albert Lautman’s work
The terms “duality” and “dual” appear repeatedly in the writings of the mathematical philosopher and World War II French Resistance fighter Albert...
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Duality for Poincaré series of surfaces and delta invariant of curves
In this article we study the delta invariant of reduced curve germs via topological techniques. We describe an explicit connection between the delta...
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Marshall Stone and duality: from differential equations to Boolean algebras
In this chapter, we investigate the contributions of Marshall Stone (1903-1989) to the study of phenomena of duality in mathematics. In fact, Stone’s...
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Duality theorems for current groups
The classical Peter—Weyl theorem describes the structure of the space of functions on a semi-simple algebraic group. On the level of characters (in...
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Tannaka Tadao‘s 1938 paper on the duality of noncommutative topological groups and its historical background
The study of the interplay between a group and the category of its representations has come to be called Tannaka duality theory (Joyal and Street,...
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ENHANCED CALCULUS AND FENCHEL DUALITY
A large part of this chapter continues develo** generalized differential calculus started in the previous chapter, but from different perspectives....
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Homotopy ribbon concordance and Alexander polynomials
We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L , then the Alexander polynomial of L divides the Alexander...
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Ringel Duality for Extended ZigZag Schur Algebra
Extended zigzag Schur algebras are quasi-hereditary algebras which are conjecturally Morita equivalent to RoCK blocks of classical Schur algebras. We...
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Poincaré Duality Relative to a Base Space
In this chapter we extend the concepts of Orientability, Differential Form with Compact Support, Integration and Poincaré Adjunctions from manifolds...
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Equivariant Poincaré Duality
We begin extending the definitions and terminology of Sect. 2.1 , by replacing the field...
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Introduction
The word “duality” is used in modern mathematics for many different phenomena. Some of these have been recognized long ago in history, albeit under...