A duality on simplicial complexes.
A functional S-dual in a strong shape category
In the S-category (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 , turns out to be of the same weak homotopy type as an appropriately defined functional dual (Corollary 4.9). Sometimes the functional object is of the same weak homotopy type as the “real” function space (§5).
A note on closed -cells in
A note on strong Jordan separation.
A Poincaré duality type theorem for polyhedra
If is a -dim polyhedran, then using geometric techniques, we construct groups and such that there are natural isomorphisms and which induce an intersection pairing. These groups give a geometric interpretation of two spectral sequences studied by Zeeman and allow us to prove a conjecture of Zeeman about them.
A strong shape theory with S-duality
Alexander duality, gropes and link homotopy.
Algebraic models of Poincaré embeddings.
An indecomposable -complex. II.
Complexe dualisant et théorèmes de dualité en géométrie analytique complexe
Dualité dans la cohomologie des espaces localement compacts
End homolgy and duality.
Finite topological spaces.
We show that the study of topological T0-spaces with a finite number of points agrees essentially with the study of polyhedra, by means of the geometric realization of finite spaces. In this paper all topological spaces are assumed to be T0.
Intersections of separators and essential submanifolds of
La théorie des rétracts approximatifs et le théorème des points fixes de Lefschetz [Book]
Les théorèmes de dualité en topologie
Linking pairings on singular spaces.
On construction of signature of quadratic forms on infinite-dimensional abstract spaces.
Poincaré duality and commutative differential graded algebras
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.
Poincaré Duality and Groups of Type (FP).