We show that the Gromov-Lawson-Rosenberg conjecture for the Semi-Dihedral group of order 16 is true.

When can two fibrewise maps be deformed in a fibrewise fashion until they are coincidence free? In order to get a thorough understanding of this problem (and, more generally, of minimum numbers that are closely related to it) we study the strength of natural geometric obstructions, such as ω-invariants and Nielsen numbers, as well as the related Nielsen theory.

In the setting of sphere bundles, a certain degree map degB turns out to play a decisive role. In many explicit cases it also yields good descriptions of the set ℱ of fibrewise homotopy classes of fibrewise maps. We introduce an addition on ℱ, which is not always single valued but still very helpful. Furthermore, normal bordism Gysin sequences and (iterated) Freudenthal suspensions play a crucial role.

A series of elements of order 4 in the symplectic cobordism ring is constructed.

In this paper we construct higher two-torsion elements of all orders in the symplectic cobordism ring. We begin by constructing higher torsion elements in the symplectic cobordism ring with singularities using a geometric approach to the Adams- Novikov spectral sequence in terms of cobordism with singularities. Then we show how these elements determine particular elements of higher torsion in the symplectic cobordism ring.

We show that any differentiable involution on a closed manifold whose fixed point set is a disjoint union of odd-dimensional real projective spaces must be a bounding involution.