Higher simple structure sets of lens spaces with the fundamental group of arbitrary order

TL;DR

This paper calculates the higher simple structure sets of lens spaces with arbitrary fundamental group order, extending previous work and also determining the structure sets of their products with spheres of dimension at least 3.

Contribution

It provides a comprehensive calculation of higher simple structure sets for lens spaces with any fundamental group order, expanding the scope of existing results.

Findings

Calculated higher simple structure sets of lens spaces with arbitrary fundamental group.

Derived simple structure sets for products of lens spaces and spheres of dimension ≥ 3.

Extended previous results to include lens spaces with any fundamental group order.

Abstract

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