# On topological properties of positive complexity one spaces

## TL;DR

This paper proves that positive symplectic complexity one spaces share topological properties with Fano varieties, such as simple connectivity, Todd genus one, and vanishing odd Betti numbers.

## Contribution

It establishes topological properties of positive symplectic complexity one spaces, extending known results from Fano varieties to this broader class.

## Key findings

- Spaces are simply connected
- Todd genus equals one
- Odd Betti numbers vanish

## Abstract

Motivated by work of Fine and Panov, and of Lindsay and Panov, we prove that every closed symplectic complexity one space that is positive (e.g. positive monotone) enjoys topological properties that Fano varieties with a complexity one holomorphic torus action possess. In particular, such spaces are simply connected, have Todd genus equal to one and vanishing odd Betti numbers.