On the Čech and axiomatic cohomology of product spaces
On the classification of Moore algebras and their deformations.
On the complex of Sobolev spaces associated with an abstract Hilbert complex.
On the construction of the Kan loop group.
On the derived category of sheaves on a manifold.
On the homology of mapping spaces
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
On the homology of small categories and asynchronous transition systems.
On the homotopy type of a chain algebra.
On the homotopy type of (n-1)-connected (3n+1)-dimensional free chain Lie algebra
Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ⊒Q, then p=∞. Denote by DGL nnp, n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL nnp. In this work we intend to answer the following two questions: Given an object (L(V), ϖ) in DGL n3n+2 and denote by S(L(V), ϖ) the class of objects homotopy equivalent...
On the locally finite chain algebra of a proper homotopy type.
On the Novikov complex for rational Morse forms
On the Number of Faces of Simplicial Complexes and the Purity of Frobenius.
On the preservation of homotopy invariance by Kan extensions
On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.
On the topological structure of a monoid on a manifold with boundary.
On total homology
On weak -homotopy equivalences of modules
Si definisce il gruppo di —omotopia di un singolo modulo e si introduce la nozione di equivalenza -omotopica debole. Sotto determinate condizioni per l'anello di base oppure per i moduli considerati, le equivalenze -omotopiche deboli coincidono con le equivalenze -omotopiche (forti).
Optimal decision trees on simplicial complexes.
Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups
Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum as an alternating sum of p-localised spectra for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We...
Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency.