ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 19, 55, 57 Muranov, Yuri V., Vladimir State University, Russia Surgery and splitting obstruction groups for one-sided submanifolds Let f : M → Y be a (simple) homotopy equivalence of n-manifolds and X ⊂ Y be a one-sided submanifold. The splitting obstruction groups LS_{n−1}(F) are defined. If f is a normal map of degree 1, then the surgery obstruction groups for the manifold pair LP_{n−1}(F) are defined. Here F is the square of fundamental groups. The relations between the LP_{∗}-groups, the L_{∗}- groups, and the splitting obstruction groups for the case of the epimorphism π_{1}(X) → π_{1}(Y) will be presented. Part of these results is joint work with D. Repovs̆. Reference: Yu. V. Muranov, D. Repovs̆, D., Surgery and splitting obstruction groups for manifold pairs, Mat. Sb. 188 (1997), 127–142.