On fake lens spaces with the fundamental group of order a power of 2

TL;DR

This paper classifies fake lens spaces of dimension ≥5 with fundamental groups of order 2^K, extending previous results from the case N=2 to higher powers of 2.

Contribution

It provides a comprehensive classification of fake lens spaces with cyclic fundamental groups of order 2^K for dimensions ≥5, generalizing earlier work for N=2.

Findings

Complete classification for N=2^K in dimensions ≥5

Extension of Wall's results to higher powers of 2

New invariants or criteria for distinguishing fake lens spaces

Abstract

We present a classification of fake lens spaces of dimension greater or equal to 5 which have as fundamental group the cyclic group of order N = 2^K, in that we extend the results of Wall and others in the case N=2.