Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the triality theory holds strongly in the tri-duality form as it was originally proposed. Otherwise, both the canonical min-max duality and the double-max duality still...

We prove an embedding theorem for maps from a finite complex into a Poincaré duality space. The proof uses fiberwise homotopy theory.

We introduce sheaves and sheaf cohomology and use them to prove the Riemann-Roch theorem and Serre duality. The main proofs follow the treatment in Forster [3].

In this paper a general coset construction for an arbitrary vertex operator algebra is studied and a duality theorem of Schur-Weyl type is obtained.

A closed 4-manifold (or, more generally, a finite PD4space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a PD3-complex. A Poincaré duality space is a space X of the homotopy type of a cell complex which satisfies Poincaré duality w...

Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen–Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial ideals. It is unclear whether researchers thinking about this topic have, to this point, been aware of the full spectrum of related developments. Therefore,...

In the S-category P (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual DX, X = (X,n) ∈ P, turns out to be of the same weak homotopy type as an appropriately defined functional dual (S0)X (Corollary 4.9). Sometimes th...

Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S = End(RU ) satisfying the condition that each finitely presented left R-module X with ExtR(X,U )= 0 for any i ≥ 1 is U -torsionless. If M is a finitely presented left R-module such that ExtR(M,U )= 0 for any i ≥ 0 with i 6= n (where n is a nonnegative integer), then ExtS(Ext n R(M,U ),U ) ∼= M and...