1671. Invariants of multi-linkoidsBoštjan Gabrovšek, Neslihan Gügümcü, 2023, izvirni znanstveni članek Povzetek: In this paper, we extend the definition of a knotoid to multilinkoids that consist of a finite number of knot and knotoid components. We study invariants of multi-linkoids, such as the Kauffman bracket polynomial, ordered bracket polynomial, the Kauffman skein module, and the $T$-invariant in relation with generalized $\Theta$-graphs. Ključne besede: knotoid, multi-linkoid, spatial graph, Kauffman bracket polynomial, Kauffman bracket skein module, theta-curve, theta-graph Objavljeno v DiRROS: 15.03.2024; Ogledov: 303; Prenosov: 160
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1674. Reflexivity of the space of transversal distributionsJure Kališnik, 2023, izvirni znanstveni članek Povzetek: For any smooth, Hausdorff and second-countable manifold $N$ one can define the Fréchet space ${\mathcal C}^{\infty}(N)$ of smooth functions on $N$ and its strong dual ${\cal E}'(N)$ of compactly supported distributions on $N$. It is a standard result that the strong dual of ${\cal E}'(N)$ is naturally isomorphic to ${\mathcal C}^{\infty}(N)$, which implies that both ${\mathcal C}^{\infty}(N)$ and ${\cal E}'(N)$ are reflexive locally convex spaces. In this paper we generalise that result to the setting of transversal distributions on the total space of a surjective submersion $\pi : P\to M$. We show that the strong ${\mathcal C}^{\infty}_c(M)$-dual of the space ${\cal E}'_{\pi} (P)$ of $\pi$-transversal distributions is naturally isomorphic to the ${\mathcal C}^{\infty}_c(M)$-module ${\mathcal C}^{\infty}(P)$. Ključne besede: distributions with compact support, Fréchet spaces, transversal distributions, homomorphisms of modules, reflexive modules Objavljeno v DiRROS: 15.03.2024; Ogledov: 383; Prenosov: 187
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1675. Rigidity of terminal simplices in persistent homologyAleksandra Franc, Žiga Virk, 2023, izvirni znanstveni članek Povzetek: Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on $\varepsilon > 0$ implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through $\varepsilon$-perturbations of filtration function. The condition for a homology class or a bar in dimension $n$ depends only on the barcodes in dimensions $n$ and $n+1$. Ključne besede: persistent homology, stability theorem, terminal simplex, rigidity Objavljeno v DiRROS: 15.03.2024; Ogledov: 321; Prenosov: 160
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