The Borel conjecture for manifolds with virtually solvable fundamental groups

TL;DR

This paper discusses the Borel conjecture for manifolds with virtually solvable fundamental groups but has been withdrawn due to issues in the proof, with results to be clarified in future work.

Contribution

The paper attempts to address the Borel conjecture for a specific class of manifolds but currently lacks a complete proof due to unresolved issues.

Findings

Proof of Lemma 3.8 does not apply to the unrestricted wreath product case

Uncertainty remains on completing the proof of Theorem 3.1

Results are pending further clarification in future work

Abstract

The article has been withdrawn by the author. Wolfgang Lueck and Peter Linnell pointed out that the proof of Lemma 3.8 does not apply to the unrestricted case of wreath product. It is not clear at this stage how to complete the proof of Theorem 3.1 using the present version of Lemma 3.8. The valid results originating from this article will be added in a later paper.