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Rank-2 wobbly bundles from special divisors on spectral curves
Duong Dinh
https://arxiv.org/abs/2406.04224 https://arxiv.org/pdf/2406…

Rank-2 wobbly bundles from special divisors on spectral curves
Let $X$ be a compact connected Riemann surface of genus $g \geq 3$ and $S \rightarrow X$ a $2:1$ branched covering defined by a generic quadratic differential on $X$. In the following notes, we explore how taking direct images of line bundles defined by certain distinguished special divisors on $S$ gives rank-2 bundles having nilpotent Higgs fields on $X$. The key ingredient is the notion of Baker-Akhiezer divisors associated to Higgs bundles and choices of subbundles of the underlying rank-2 b…

More on Landau's theorem and Conjugacy Classes
Burcu \c{C}{\i}narc{\i}, Thomas Michael Keller, Attila Mar\'oti, Iulian I. Simion
https://arxiv.org/abs/2406.11199

More on Landau's theorem and Conjugacy Classes
Let $p$ be a prime. We construct a function $f$ on the natural numbers such that $f(x) \to \infty$ as $x \to \infty$ and $k_{p}(G)+k_{p'}(G)\geq f(|G|)$ for all finite groups $G$. Here $k_{p}(G)$ denotes the number of conjugacy classes of nontrivial $p$-elements in $G$ and $k_{p'}(G)$ denotes the number of conjugacy classes of elements of $G$ whose orders are coprime to $p$. This is a variation of an old theorem of Landau and is used to prove the following: There exists a number $c$ s…

This https://arxiv.org/abs/2404.01674 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

PRISM-TopoMap: Online Topological Mapping with Place Recognition and Scan Matching
Mapping is one of the crucial tasks enabling autonomous navigation of a mobile robot. Conventional mapping methods output dense geometric map representation, e.g. an occupancy grid, which is not trivial to keep consistent for the prolonged runs covering large environments. Meanwhile, capturing the topological structure of the workspace enables fast path planning, is less prone to odometry error accumulation and does not consume much memory. Following this idea, this paper introduces PRISM-TopoM…