Andrea Bianchi

activity

20172026

most citedSplitting of the homology of the punctured mapping class group

8 citations · 26 across the 17 of their papers we have counts for

collaborators

19 papers

math.AT2026

Stable rational cohomology splitting of moduli of branched covers of curves

Andrea Bianchi

We consider the moduli stack $H_{g, d}$ parametrising maps $θ : C \to L$ of degree $d$ between complex curves of genera $g$ and $0$ . We provide a splitting of the stabl…

math.AT2026

Stable homology of complex braid groups

Andrea Bianchi, Filippo Callegaro, Luigi Caputi +1

We compute the stable homology of complex braid groups of types $B (e, e, n)$ and $B (2 e, e, n)$ for fixed $e \geq 2$ and increasing $n$ . This accounts for the stable homology of all infini…

math.KT2024

Segal K-theory of vector spaces with an automorphism

Andrea Bianchi, Florian Kranhold

We describe the Segal $K$ -theory of the symmetric monoidal category of finite-dimensional vector spaces over a perfect field $F$ together with an automorphism, or, equival…

math.AT2023

Homology of configuration spaces of surfaces modulo an odd prime

Andrea Bianchi, Andreas Stavrou

For a compact orientable surface $Σ_{g, 1}$ of genus $g$ with one boundary component and for an odd prime number $p$ , we study the homology of the unordered configuration spaces $C_…

math.AT2023

Polynomial stability of the homology of Hurwitz spaces

Andrea Bianchi, Jeremy Miller

For a finite group $G$ and a conjugation-invariant subset $Q \subseteq G$ , we consider the Hurwitz space $Hur_{n} (Q)$ parametrising branched covers of the plane with $n$ bran…

math.GT2022

Non-trivial action of the Johnson filtration on the homology of configuration spaces

Andrea Bianchi, Andreas Stavrou

We let the mapping class group $Γ_{g, 1}$ of a genus $g$ surface $Σ_{g, 1}$ with one boundary component act on the homology $H_{*} (F_{n} (Σ_{g, 1}); Q)$ of the $n^{t h}$ ordered c…

math.AC2022★ 1 cited

On Generators and Relations of the Rational Cohomology of Hilbert Schemes

Andrea Bianchi, Alexander Mangulad Christgau, Jonathan Sejr Pedersen

We consider for $d \geq 1$ the graded commutative $Q$ -algebra $A (d) := H^{*} (Hilb^{d} (C^{2}); Q)$ , which is also connected to the study of…

math.AT2021★ 3 cited

Moduli spaces of Riemann surfaces as Hurwitz spaces

Andrea Bianchi

We consider the moduli space $M_{g, n}$ of Riemann surfaces of genus $g \geq 0$ with $n \geq 1$ ordered and directed marked points. For $d \geq 2 g + n - 1$ we show that $\mathfrak{M}…

math.AT2021★ 2 cited

Deloopings of Hurwitz spaces

Andrea Bianchi

For a partially multiplicative quandle (PMQ) $Q$ we consider the topological monoid $HM ˚ (Q)$ of Hurwitz spaces of configurations in the plane…

math.AT2021★ 2 cited

Hurwitz-Ran spaces

Andrea Bianchi

Given a couple of subspaces $Y \subset X$ of the complex plane $C$ satisfying some mild conditions (a ``nice couple''), and given a PMQ-pair $(\mathcal{Q…

math.AT2021★ 1 cited

Partially multiplicative quandles and simplicial Hurwitz spaces

Andrea Bianchi

We introduce partially multiplicative quandles (PMQ), a generalisation of both partial monoids and quandles. We set up the basic theory of PMQs, focusing on the properties of free…

math.AT2021★ 2 cited

Parametrised moduli spaces of surfaces as infinite loop spaces

Andrea Bianchi, Florian Kranhold, Jens Reinhold

We study the $E_{2}$ -algebra $Λ M_{*, 1} = ∐_{g ⩾ 0} Λ M_{g, 1}$ consisting of free loop spaces of moduli spaces of Riemann surfaces with one parametrised…

math.GT2021

Mapping class group actions on configuration spaces and the Johnson filtration

Andrea Bianchi, Jeremy Miller, Jennifer C. H. Wilson

Let $F_{n} (Σ_{g, 1})$ denote the configuration space of $n$ ordered points on the surface $Σ_{g, 1}$ and let $Γ_{g, 1}$ denote the mapping class group of $Σ_{g, 1}$ . We prove that the ac…

math.AT2021★ 1 cited

Vertical configuration spaces and their homology

Andrea Bianchi, Florian Kranhold

We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $R^{d}$ , where points in each cluster satisfy a 'verticality' condition…

math.AT2020★ 1 cited

An upper bound on the topological complexity of discriminantal varieties

Andrea Bianchi

We give an upper bound on the topological complexity of varieties $V$ obtained as complements in $C^{m}$ of the zero locus of a polynomial. As an application, we d…

math.AT2019

On the homology of the commutator subgroup of the pure braid group

Andrea Bianchi

We study the homology of $[P_{n}, P_{n}]$ , the commutator subgroup of the pure braid group on $n$ strands, and show that $H_{l} ([P_{n}, P_{n}])$ contains a free abelian group of infinite rank…

math.AT2019★ 8 cited

Splitting of the homology of the punctured mapping class group

Andrea Bianchi

Let $Γ_{g, 1}^{m}$ be the mapping class group of the orientable surface $Σ_{g, 1}^{m}$ of genus $g$ with one parametrised boundary curve and $m$ permutable punctures; when $m = 0$ we omit…

math.AT2019

Braid groups, mapping class groups and their homology with twisted coefficients

Andrea Bianchi

We consider the Birman-Hilden inclusion $φ : Br_{2 g + 1} \to Γ_{g, 1}$ of the braid group into the mapping class group of an orientable surface with boundary, and prove th…

math.AT2017★ 5 cited

Topological complexity of unordered configuration spaces of surfaces

Andrea Bianchi, David Recio-Mitter

We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for th…