Tootfinder

Bigraded Lie algebras and nilpotent fundamental groups of smooth complex algebraic varieties
Taito Shimoji
https://arxiv.org/abs/2510.09026 https://arxiv.o…

Bigraded Lie algebras and nilpotent fundamental groups of smooth complex algebraic varieties
Let $X$ be a smooth complex algebraic variety. Assume that the fundamental group $π_1(X,x)$ is torsion-free nilpotent. We show that if the betti number $b_1(X)$ is less than or equal to $3$, then $π_1(X,x)$ is isomorphic to $\mathbb{Z}$, $\mathbb{Z}^2$, $\mathbb{Z}^3$, a lattice in the Heisenberg group $H_3(\mathbb{R})$ or $\mathbb{R}\times H_3(\mathbb{R})$. Moreover we show that $π_1(X,x)$ is abelian or $2$-step nilpotent if the rank of $π_1(X,x)$ is less than or equal to seven. We prove t…

Quasi-conformal VS quasi-isometric equivalence in spaces with controlled growth
Katrin F\"Assler, Enrico Le Donne, Sebastiano Nicolussi Golo, Alessandro Ottazzi, Pierre Pansu
https://arxiv.org/abs/2510.12161

Quasi-conformal VS quasi-isometric equivalence in spaces with controlled growth
We study conditions under which quasi-conformal homeomorphisms are quasi-isometries. We show that if two nilpotent geodesic Lie groups are quasi-conformally homeomorphic, then they are quasi-isometrically equivalent. We also give more general results beyond the nilpotent case. In particular, we show that quasi-conformal homeomorphisms between geodesic Lie groups are quasi-isometries whenever the spaces have strict parabolic or hyperbolic conformal type. As a consequence, quasi-conformal homeomo…

Positive Hermitian curvature flow on 2-step nilpotent Lie groups
Ettore Lo Giudice
https://arxiv.org/abs/2510.08846 https://arxiv.org/pdf/2510.08846…

Positive Hermitian curvature flow on 2-step nilpotent Lie groups
We study the positive Hermitian curvature flow for left-invariant metrics on $2$-step nilpotent Lie groups with a left-invariant complex structure $J$. We describe the long-time behavior of the flow under the assumption that $J[\mathfrak{g}, \mathfrak{g}]$ is contained in the center of $\mathfrak{g}$. We show that under our assumption the flow $g_{t}$ exists for all positive $t$ and $(G,(1+t)^{-1}g_{t})$ converges, in the Cheeger-Gromov topology, to a $2$-step nilpotent Lie group with a non fla…

Spectral and Nilpotent Matrix Orderings: Comparison and Applications in Dynamic Systems
Shih-Yu Chang
https://arxiv.org/abs/2510.08579 https://arxiv.org/pd…

Spectral and Nilpotent Matrix Orderings: Comparison and Applications in Dynamic Systems
In our earlier work, we proposed the \emph{Spectral and Nilpotent Ordering} (SNO) as a new framework that extends matrix comparison beyond the Hermitian setting by incorporating both spectral and nilpotent structures. Building on that foundation, the present paper develops concrete certificates and applications of SNO. First, we employ generalized Gershgorin theorems to design certificates for spectral ordering that avoid direct eigenvalue computation and analyze their robustness under perturba…

"One peculiarity of this revamped public provision is that it is happening without significant economic growth and without being fuelled by debt. Instead, it is reliant on budget restructuring and increased tax collection."
Edwin F. Ackerman, Sheinbaum’s Mission — Sidecar
https://newleftreview.or…

Edwin F. Ackerman, Sheinbaum’s Mission — Sidecar
The Mexican President’s first year.

ConPoSe: LLM-Guided Contact Point Selection for Scalable Cooperative Object Pushing
Noah Steinkr\"uger, Nisarga Nilavadi, Wolfram Burgard, Tanja Katharina Kaiser
https://arxiv.org/abs/2510.08705

ConPoSe: LLM-Guided Contact Point Selection for Scalable Cooperative Object Pushing
Object transportation in cluttered environments is a fundamental task in various domains, including domestic service and warehouse logistics. In cooperative object transport, multiple robots must coordinate to move objects that are too large for a single robot. One transport strategy is pushing, which only requires simple robots. However, careful selection of robot-object contact points is necessary to push the object along a preplanned path. Although this selection can be solved analytically, …

Crosslisted article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Bigraded Lie algebras and nilpotent fundamental groups of smooth complex algebraic varieties
Taito Shimoji

Rost nilpotence for twisted Milnor hypersurfaces
Charles De Clercq, Evan Marth, Kirill Zainoulline
https://arxiv.org/abs/2510.07095 https://arxiv.org/pdf/2…

Rost nilpotence for twisted Milnor hypersurfaces
We show that the strong Rost nilpotence holds for motives of generic hyperplane sections of twisted Milnor hypersurfaces. Hence, we provide a new family of examples of smooth projective algebraic varieties which satisfy the strong Rost nilpotence principle. As an application, we compute the $p$-canonical dimension for such varieties.

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Infinite dimensional analogues of nilpotent and solvable Lie algebras
F. H. Haydarov, B. A. Omirov, G. O. Solijanova
https://arxiv.org/abs/2510.02488 https://

Infinite dimensional analogues of nilpotent and solvable Lie algebras
We study infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable Lie algebras. We extend classical triangularization results (Engel's and Lie's theorems) to the pro-setting and establish existence results for the pro-nilpotent radical in pro-solvable algebras and in certain residually solvable algebras. We adapt finite-dimensional construction methods to produce residually solvabl…