On the elements of the second type in surgery groups

In 1987 Kharshiladze introduced the concept of type for an element in a Wall group, and proved that the elements of the first and second type cannot be realized by normal maps of closed manifolds. In the present paper we give a geometrical interpretation of this approach by using the Browder-Quinn surgery obstruction groups for filtered manifolds. Then we study some algebraic and geometrical properties of the elements of the second type, and apply the obtained results for computing the assembly map for some classes of groups. Further applications about the realization problem of the surgery and splitting obstructions complete the paper.