Rigidity of powers and Kosniowski's conjecture

TL;DR

This paper investigates a problem related to the rigidity of powers in topology, providing solutions for specific cases and confirming Kosniowski's conjecture in certain low-dimensional scenarios.

Contribution

It introduces an elementary formulation of the rigidity problem and proves the conjecture for dimensions less than 11 or equal to 14.

Findings

Kosniowski's conjecture holds for dimensions <11 or =14.

The problem on rigidity of powers is solved in particular cases.

An elementary approach is used without advanced algebraic topology.

Abstract

In this paper we state a problem on rigidity of powers, which has a strong topological background for the rigid Hirzebruch genera and Kosniowski's conjecture of unitary circle actions. However, our statement of this problem is elementary enough and does not require any knowledge of algebraic topology. We shall give a solution of this problem for some particular cases. As a consequence, we obtain that Kosniowski's conjecture holds in the case of dimension less than 11 or equal to 14.