On the suspension homomorphism
In this paper we investigate the conditions for the suspension homomorphism is onto or an isomorphism.
On the Weak Covering Homotopy Property.
On the Whitehead Theorem in shape theory
On the Whitehead theorem in shape theory I
On the Whitehead theorem in shape theory II
On three types of simplicial objects
On weak homotopy
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).
On weak monomorphisms and weak epimorphisms in the category of pro-groups.
In this paper we characterize weak monomorphisms and weak epimorphisms in the category of pro-groups. Also we define the notion of weakly exact sequence and we study this notion in the category of pro-groups.
On Whitehead's inequality, .
On Yetter's invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups.
On Δ-spaces and fundamental dimension in the sense of Borsuk
Open/Closed string topology and moduli space actions via open/closed Hochschild actions.
Opérades cellulaires et espaces de lacets itérés
L’espace des configurations de points distincts de admet une filtration naturelle qui est induite par les inclusions des dans . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.
Operads for -ary algebras – calculations and conjectures
In [8] we studied Koszulity of a family of operads depending on a natural number and on the degree of the generating operation. While we proved that, for , the operad is Koszul if and only if is even, and while it follows from [4] that is Koszul for even and arbitrary , the (non)Koszulity of for odd and remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.
Operads in iterated monoidal categories.
Operády v současné matematice
Operations and co-operations in Morava -theory.
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Parallelizability of Finite H-Spaces.