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Research
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7,971+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
It is not known whether the realisation part of the $s$-cobordism theorem holds for smooth 4-manifolds, nor whether every pair of smoothly $h$-cobordant 4-manifolds is also smoothly $s$-cobordant. We …
We extend the classification results for torsion classes and torsion-free classes in the category of finitely generated modules over a commutative noetherian ring to suitable symmetric monoidal closed…
Building on the author's earlier work on topological and abstract expansivity, this paper introduces and explores the notion of algebraic expansivity for endomorphisms of abelian groups. We analyze th…
In this article, we find finitely many numerical invariants to classify the diffeomorphism types of three dimensional simply connected Mori fibre spaces with torsion free homology groups.…
We extend the refined asymptotics of analytic torsion associated to congruence subgroups of $\operatorname{SL}(n)$ in previous work, to congruence subgroups in a large family of reductive groups. This…
We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we p…
A finite Euclidean set is diameter-Ramsey if, for every number of colors, some finite same-diameter witness has the property that every coloring of the witness contains a monochromatic congruent copy …
Using the higher covariant derivative on a manifold $ M $ equipped with a torsion-free connection, we define a natural surjective bundle map $ \Phi $ from $ (\otimes(TM))\otimes (\wedge(TM)) $ to the …
For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for well-separated $\kap…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao o…
For a topological space that is homeomorphic to a finite simplicial complex, we prove that the Bartels--Nikolaus assembly functor has a fully faithful right adjoint. Using this, we define for each suc…
Corsten and Frankl conjectured that a simplex is diameter-Ramsey if and only if its circumcenter lies in its convex hull. We disprove this conjecture in every dimension $d\ge 3$. The main tool is a su…
We present a geometric framework for reconstruction problems based on Vaisman foliations and Atiyah--Molino sequences. Independent projections induce transverse foliations and dual connections; vanish…
We describe the prismatic F-gauge associated to a finite flat height one group scheme over a smooth variety of positive characteristic. As applications, we derive the description of the crystalline Di…
This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely …
We study $v_n$-periodic phenomena in $C_2$-equivariant stable homotopy through the lens of the $C_2$-equivariant Adams spectral sequence at the prime 2. In particular, we construct/detect certain clas…
Koll\'{a}r showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K…
The triple-cup product form $\mu$ is a classical invariant of $3$-manifolds, determining the cohomology ring up to torsion. Given a closed, connected, oriented $3$-manifold $M$, we describe an explici…
We introduce and study small covers that are pullbacks from the simplex, extending pullbacks from the linear model. Our main result gives several equivalent characterizations of this class, including …
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