Tootfinder

Homological growth of nilpotent-by-abelian pro-p groups
Dessislava H. Kochloukova, Aline G. S. Pinto
https://arxiv.org/abs/2510.00421 https://arxiv.org/pdf…

Homological growth of nilpotent-by-abelian pro-p groups
We show that the torsion-free rank of $H_i(M, \mathbb{Z}_p)$ has finite upper bound for $i \leq m$, where $M$ runs through the pro-$p$ subgroups of finite index in a pro-$p$ group $G$ that is (nilpotent of class $c$)-by-abelian such that $ G/N'$ is of type $FP_{2cm}$.

Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://arxiv.org/abs/2510.00159 https://arxiv.org/pdf/2510.00159

Volumes of Nullhomotopies in Nilpotent Spaces
The Shadowing Principle of Manin has proved a valuable tool for addressing questions of quantitative topology raised by Gromov in the late 1900s. The principle informally provides a way for bounded algebraic maps between differential graded algebras to be translated into nearby genuine maps between their geometric realizations. We extend this principle to finite towers of principal $K(G,n)$ fibrations, and in particular apply this construction to nilpotent spaces. As a specific application of t…

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Higher-order exceptional points unveiled by nilpotence and mathematical induction
Kenta Takata, Adam Mock, Masaya Notomi, Akihiko Shinya
https://arxiv.org/abs/2510.00623 https:/…

Higher-order exceptional points unveiled by nilpotence and mathematical induction
Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of $n$ degenerate states is said to have order $n$, and higher-order EPs (HEPs) with $n \ge 3$ exhibit rich intrinsic features potential for applications. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence a…

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Crosslisted article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://

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Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://

The spectral Sullivan conjecture
Ishan Levy
https://arxiv.org/abs/2510.00262 https://arxiv.org/pdf/2510.00262

The spectral Sullivan conjecture
We show that any map from an infinite loop space to a $p$-complete nilpotent finite dimensional space factors canonically through a union of $p$-adic tori. This is proven via bootstrapping from the case of $B\mathbb{Z}/p\mathbb{Z}$, which is the key case of the Sullivan conjecture proven by Miller. The main step in our proof is to show that the subcategory of spectra generated by the reduced suspension spectrum of $B\mathbb{Z}/p\mathbb{Z}$ under colimits and extensions agrees with that of a Moo…

The Tits alternative for visibility spaces
Ran Ji, Yunhui Wu
https://arxiv.org/abs/2510.01008 https://arxiv.org/pdf/2510.01008

The Tits alternative for visibility spaces
Let $Γ$ be a finitely generated group acting properly discontinuously by isometries on a visibility CAT(0) space $X$ that satisfies the bounded packing property. We prove that $Γ$ satisfies the Tits alternative: it is either almost nilpotent or contains a free nonabelian subgroup of rank $2$. In the former case, it is equivalent to that the cardinality of the limit set of $Γ$ in the geometric boundary of $X$ is no greater than $2$. As an application of the Tits alternative, we show that any …