A proof of Kosniowski conjecture

TL;DR

This paper proves the Kosniowski conjecture by establishing a new inequality relating the Euler characteristic and dimension of certain unitary $S^1$-manifolds with isolated fixed points.

Contribution

It provides a rigorous proof of the Kosniowski conjecture, confirming the inequality between Euler characteristic and dimension for these manifolds.

Findings

Proves that 4 times the Euler characteristic exceeds the dimension of the manifold.

Confirms the Kosniowski conjecture for unitary $S^1$-manifolds with isolated fixed points.

Establishes a fundamental inequality in equivariant topology.

Abstract

Let $M$ be a unitary $S^1$-manifold with only isolated fixed points such that $M$ is not a boundary. We show that $4\chi(M)>\dim M$, where $\chi(M)$ is the Euler characteristic of $M$. This gives an affirmative answer of Kosniowski conjecture.