Higher simple structure sets of lens spaces with the fundamental group of order $2^K$

TL;DR

This paper computes the higher simple structure sets of lens spaces with fundamental groups of order a power of two, extending previous work and also determining the structure sets of certain product spaces.

Contribution

It provides new calculations of higher simple structure sets for lens spaces with 2-power order fundamental groups and their products with spheres.

Findings

Calculated higher simple structure sets for lens spaces with 2-power order fundamental groups

Derived simple structure sets for products of these lens spaces with spheres

Extended existing results in surgery theory for specific classes of manifolds

Abstract

Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory in the case when the fundamental group has order a power of $2$. As a corollary we also obtain a calculation of the simple structure set of the products of lens spaces and spheres of dimension grater or equal to $3$ in this case.