Year: 2025
Type: article
Abstract: This paper contains some results about the topology of $$\mathcal {M}_{0,n+1}/\Sigma _n$$ M 0 , n + 1 / Σ n , where $$\mathcal {M}_{0,n+1}$$ M 0 , n + 1 is the moduli space of genus zero Riemann surfaces with marked points. We show that $$\mathcal {M}_{0,n+1}/\Sigma _n$$ M 0 , n + 1 / Σ n is not a topological manifold for $$n\ge 4$$ n ≥ 4 , and it is simply connected for any $$n\in \mathbb {N}$$ n ∈ N . We also present some homology computations: for example we show that $$\mathcal {M}_{0,p+1}/\Sigma _p$$ M 0 , p + 1 / Σ p has no p torsion, where p is a prime. Lastly we compute $$H_*(\mathcal {M}_{0,n+1}/\Sigma _n;\mathbb {Z})$$ H ∗ ( M 0 , n + 1 / Σ n ; Z ) for small values of n , proving that $$\mathcal {M}_{0,n+1}/\Sigma _n$$ M 0 , n + 1 / Σ n is contractible for $$n\le 5$$ n ≤ 5 while $$\mathcal {M}_{0,7}/\Sigma _6$$
Author: Tommaso Rossi
Institution: University of Rome Tor Vergata
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Awards: G2806466947, G689437076
OpenAlex ID: W4415772836