It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family $w_{\alpha }^H\left(X\right)$ of elements of the groups $K_0\left(\mathbb{Z}\left[{\pi }_0{\left(WH\left(X\right)\right)}_{\alpha }^{*}\right]\right)$. We prove that every family $w_{\alpha }^H$ of elements of the groups $K_0\left(\mathbb{Z}\left[{\pi }_0{\left(WH\left(X\right)\right)}_{\alpha }^{*}\right]\right)$ can be realized as the family of equivariant finiteness obstructions $w_{\alpha }^H\left(X\right)$ of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall’s obstruction...

In questo articolo si riassumono le definizioni e le principali proprietà dei gruppi di ostruzione con decorazione di tipo LS e LP. Si stabiliscono nuove relazioni fra questi gruppi e si descrivono le proprietà delle mappe naturali fra differenti gruppi con decorazione. Si costruiscono varie successioni spettrali, contenenti questi gruppi con decorazione, e si studiano la loro connessione con le successioni spettrali in $K$-teoria per certe estensioni quadratiche di antistrutture. Infine, si introduce...

We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.

For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group $L{P}_{*}$ generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the...