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Displaying 41 – 57 of 57

Smoothing H-spaces II.

Erik Kjaer Pedersen (1980)

Mathematica Scandinavica

Some surgery formulae for maps into $Ω^{\infty} S^{\infty} (R P^{\infty})$

Ryszard Rubinsztein (1983)

Fundamenta Mathematicae

Splitting obstructions and properties of objects in the Nil categories

Tadeusz Koźniewski (1999)

Fundamenta Mathematicae

We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.

Surgery on pairs of closed manifolds

Alberto Cavicchioli, Yuri V. Muranov, Fulvia Spaggiari (2009)

Czechoslovak Mathematical Journal

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...