Tootfinder

Bordism from quasi-isomorphism
Noah Porcelli, Ivan Smith
https://arxiv.org/abs/2509.21587 https://arxiv.org/pdf/2509.21587…

Bordism from quasi-isomorphism
Let $X$ be a graded Liouville domain. Fix a pair of infinite loop spaces $Ψ= (Θ\to Φ)$ living over $(BO \to BU)$. This determines a spectral Fukaya category $\mathcal{F}(X;Ψ)$ whenever $TX$ lifts to $Φ$, containing closed exact Lagrangians $L$ for which $TL$ lifts compatibly to $Θ$; and by Bott periodicity and index theory, a Thom spectrum $R$ with bordism theory $R_*$. Suppose that $L$ and $K$ are quasi-isomorphic in the Fukaya category over $\mathbb{Z}$. We prove that: (a) if both l…

Open-closed maps and spectral local systems
Noah Porcelli, Ivan Smith
https://arxiv.org/abs/2509.21483 https://arxiv.org/pdf/2509.21483

Open-closed maps and spectral local systems
Let $X$ be a graded Liouville domain. Fix a pair of infinite loop spaces $Ψ= (Θ\to Φ)$ living over $(BO \to BU)$. This determines a spectral Fukaya category $\mathcal{F}(X;Ψ)$ whenever $TX$ lifts to $Φ$, containing closed exact Lagrangians $L$ for which $TL$ lifts compatibly to $Θ$; and by Bott periodicity and index theory, a Thom spectrum $R$ with bordism theory $R_*$. This paper has two main goals: we incorporate rank one spectral local systems $ξ: L \to BGL_1(R)$ into the spectral c…

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves
Soheyla Feyzbakhsh, Naoki Koseki, Zhiyu Liu, Nick Rekuski
https://arxiv.org/abs/2509.24990 https…

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves
Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macrì-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on $X$, to verifying a Brill-Noether-type inequality for curves on $X$. We then prove this inequality for a broad class of Calabi-Yau threefolds, including complete intersection Calabi-Yau threefolds in weighted projective spaces.