MATHEMATICA SCANDINAVICA
https://www.mscand.dk/
en-USmscand@math.au.dk (Arne Jensen)mscand@math.au.dk (Anne Mette Christiansen)Sat, 11 Jun 2022 13:37:34 +0200OJS 3.3.0.10http://blogs.law.harvard.edu/tech/rss60The homology of the groupoid of the self-similar infinite dihedral group
https://www.mscand.dk/article/view/129708
<p>We compute the $K$-theory of the $C^*$-algebra associated to the self-similar infinite dihedral group, and the homology of its associated étale groupoid. We see that the rational homology differs from the $K$-theory, strongly contradicting a conjecture posted by Matui. Moreover, we compute the abelianization of the topological full group of the groupoid associated to the self-similar infinite dihedral group.</p>Eduard Ortega, Alvaro Sanchez
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/129708Sat, 11 Jun 2022 00:00:00 +0200Canonical subsheaves of torsionfree semistable sheaves
https://www.mscand.dk/article/view/129709
<p>Let $F$ be a torsionfree semistable coherent sheaf on a polarized normal projective variety defined over an algebraically closed field. We prove that $F$ has a unique maximal locally free subsheaf $V$ such that $F/V$ is torsionfree and $V$ also admits a filtration of subbundles for which each successive quotient is a stable vector bundle whose slope is $\mu (F)$. We also prove that $F$ has a unique maximal reflexive subsheaf $W$ such that $F/W$ is torsionfree and $W$ admits a filtration of subsheaves for which each successive quotient is a stable reflexive sheaf whose slope is $\mu (F)$. We show that these canonical subsheaves behave well with respect to the pullback operation by étale Galois covering maps. Given a separable finite surjective map $\phi \colon Y \longrightarrow X$ between normal projective varieties, we give a criterion for the induced homomorphism of étale fundamental groups $\phi _*\colon \pi ^{\textrm {et}}_{1}(Y) \longrightarrow \pi ^{\textrm {et}}_{1}(X)$ to be surjective. The criterion in question is expressed in terms of the above mentioned unique maximal locally free subsheaf associated to the direct image $\phi _*{\mathcal O}_Y$.</p>Indranil Biswas, A. J. Parameswaran
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/129709Sat, 11 Jun 2022 00:00:00 +0200A note on differences of composition operators acting on the Hardy space
https://www.mscand.dk/article/view/129748
<p>When $\varphi$ and $\psi$ are holomorphic self-maps of the unit disk with bounded multiplicity, we give a compact characterization for the difference of composition operators $C_\varphi $ and $C_\psi $ acting on the Hardy space, which extends a recent result in the case of univalent maps by Choe et al.</p>Jineng Dai
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/129748Sat, 11 Jun 2022 00:00:00 +0200Direct limits of infinite-dimensional Carnot groups
https://www.mscand.dk/article/view/132062
<p>We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot group. We also prove a Rademacher-type theorem for such limits.</p>Terhi Moisala, Enrico Pasqualetto
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132062Sat, 11 Jun 2022 00:00:00 +0200On the Liouville and strong Liouville properties for a class of non-local operators
https://www.mscand.dk/article/view/132068
<p>We prove a necessary and sufficient condition for the Liouville and strong Liouville properties of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of) the set of zeros of the characteristic exponent of the Lévy process.</p>David Berger, René L. Schilling
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132068Sat, 11 Jun 2022 00:00:00 +0200Intermediate Jacobians and the slice filtration
https://www.mscand.dk/article/view/132174
<p>For every $n$-dimensional smooth projective variety $X$ over ℂ, the motive $M(X)$ is expected to admit a Chow-Künneth decomposition $M_0(X)\oplus \cdots \oplus M_{2n}(X)$. Inspired by the slice filtration of $M(X)$ we propose the definitions of $M_2(X)$ and $M_{2n-2}(X)$. In our construction we use intermediate Jacobians.</p>Doosung Park
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132174Sat, 11 Jun 2022 00:00:00 +0200A remark on singular cohomology and sheaf cohomology
https://www.mscand.dk/article/view/132191
<p>We prove a comparison isomorphism between singular cohomology and sheaf cohomology.</p>Dan Petersen
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132191Sat, 11 Jun 2022 00:00:00 +0200Stability of non-proper functions
https://www.mscand.dk/article/view/132211
<p>The purpose of this paper is to give a sufficient condition for (strong) stability of non-proper smooth functions (with respect to the Whitney topology). We show that a Morse function is stable if it is end-trivial at any point in its discriminant, where end-triviality (which is also called local triviality at infinity) is a property concerning behavior of functions around the ends of the source manifolds. We further show that a Morse function is strongly stable if (and only if) it is quasi-proper. This result yields existence of a strongly stable but not infinitesimally stable function. Applying our result on stability, we give a sufficient condition for stability of Nash functions, and show that any Nash function becomes stable after a generic linear perturbation.</p>Kenta Hayano
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132211Sat, 11 Jun 2022 00:00:00 +0200The weak min-max property in Banach spaces
https://www.mscand.dk/article/view/132214
<p>In this paper, we investigate the relationship between the weak min-max property and the diameter uniformity of domains in Banach spaces with dimension at least 2. As an application, we show that diameter uniform domains are invariant under relatively quasimöbius mappings.</p>Zhengyong Ouyang, Antti Rasila, Tiantian Guan
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132214Sat, 11 Jun 2022 00:00:00 +0200The Perfekt theory of $M$-ideals
https://www.mscand.dk/article/view/132230
<p>We revisit some ideas of K.-M. Perfekt who has provided an elegant framework to detect the biduality between function or sequence spaces defined in terms of some $o$- respectively $O$-condition. We present new proofs under somewhat weaker assumptions than before and apply the result to Lipschitz spaces.</p>Dirk Werner
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132230Sat, 11 Jun 2022 00:00:00 +0200Geodesic families characterizing flat metrics on a cylinder and a plane
https://www.mscand.dk/article/view/132247
<p>We prove that a complete non-compact surface contains a domain which is isometric to a pipe cylinder if all prime closed geodesics in it have the same length. As an application, we show that a flat cylinder is conjugacy rigid in the class of surfaces whose universal covering planes satisfy the divergence property. We study the divergence property from the view point of geodesic conjugacy for the Euclidean plane.</p>Nobuhiro Innami, Yoe Itokawa, Tetsuya Nagano, Katsuhiro Shiohama
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https://www.mscand.dk/article/view/132247Sat, 11 Jun 2022 00:00:00 +0200Poincaré duality for tautological Chern subrings of orthogonal grassmannians
https://www.mscand.dk/article/view/132376
<p>Let $X$ be an orthogonal grassmannian of a nondegenerate quadratic form $q$ over a field. Let $C$ be the subring in the Chow ring $\text {CH}(X)$ generated by the Chern classes of the tautological vector bundle on $X$. We prove Poincaré duality for $C$. For $q$ of odd dimension, the result was already known due to an identification between $C$ and the Chow ring of certain symplectic grassmannian. For $q$ of even dimension, such an identification is not available.</p>Nikita A. Karpenko, Alexander S. Merkurjev
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https://www.mscand.dk/article/view/132376Sat, 11 Jun 2022 00:00:00 +0200Cover1
https://www.mscand.dk/article/view/132863
<p>Cover</p>Mathematica Scandinavica
Copyright (c) 2022 MATHEMATICA SCANDINAVICA
https://www.mscand.dk/article/view/132863Sat, 11 Jun 2022 00:00:00 +0200