# Kosniowski's conjecture and weights

## TL;DR

This paper confirms Kosniowski's conjecture for almost complex manifolds under specific weight conditions, establishing an upper bound on the manifold's dimension based on fixed points.

## Contribution

It proves the conjecture for almost complex manifolds with certain weight restrictions, advancing understanding of circle actions on such manifolds.

## Key findings

- Confirmed the conjecture when weights are of one type ±a
- Confirmed the conjecture when weights are of two types ±a, ±b
- Established a linear bound on the dimension based on fixed points

## Abstract

The conjecture of Kosniowski asserts that if the circle acts on a compact unitary manifold $M$ with a non-empty fixed point set and $M$ does not bound a unitary manifold equivariantly, then the dimension of the manifold is bounded above by a linear function on the number of fixed points. We confirm the conjecture for almost complex manifolds under an assumption on weights. For instance, we confirm the conjecture if there is one type $\pm a$ of weights, or there are two types $\pm a$, $\pm b$ of weights.