Multi-graded algebras associated to surface singularities

Topological Atomic Chains on 2D Hybrid Structure

Materials ◽

10.3390/ma14123289 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3289

Author(s):

Tomasz Kwapiński ◽

Marcin Kurzyna

Keyword(s):

Tight Binding ◽

Wide Band ◽

Hybrid Structure ◽

Spectral Density Function ◽

Hybrid Structures ◽

Function Technique ◽

Edge States ◽

Surface Singularities ◽

Atomic Chains ◽

Topological States

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

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Homological identities and dualizing complexes of commutative differential graded algebras

Israel Journal of Mathematics ◽

10.1007/s11856-021-2095-3 ◽

2021 ◽

Author(s):

Hiroyuki Minamoto

Keyword(s):

Graded Algebras ◽

Differential Graded Algebras ◽

Dualizing Complexes

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Homological epimorphisms, homotopy epimorphisms and acyclic maps

Forum Mathematicum ◽

10.1515/forum-2019-0249 ◽

2020 ◽

Vol 32 (6) ◽

pp. 1395-1406

Author(s):

Joseph Chuang ◽

Andrey Lazarev

Keyword(s):

Wide Class ◽

Topological Spaces ◽

Loop Spaces ◽

Graded Algebras ◽

Differential Graded Algebras ◽

Algebraic Description ◽

Acyclic Map ◽

Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

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Reflexive modules on normal surface singularities and representations of the local fundamental group

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2007.07.002 ◽

2008 ◽

Vol 212 (4) ◽

pp. 851-862 ◽

Cited By ~ 2

Author(s):

Trond Stølen Gustavsen ◽

Runar Ile

Keyword(s):

Fundamental Group ◽

Normal Surface ◽

Surface Singularities ◽

Reflexive Modules

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ON -K2 FOR NORMAL SURFACE SINGULARITIES

International Journal of Mathematics ◽

10.1142/s0129167x98000294 ◽

1998 ◽

Vol 09 (06) ◽

pp. 653-668 ◽

Cited By ~ 2

Author(s):

HAO CHEN ◽

SHIHOKO ISHII

Keyword(s):

Lower Bound ◽

Positive Integer ◽

Rational Number ◽

Accumulation Point ◽

Normal Surface ◽

Accumulation Points ◽

Surface Singularities

In this paper we show the lower bound of the set of non-zero -K2 for normal surface singularities establishing that this set has no accumulation points from above. We also prove that every accumulation point from below is a rational number and every positive integer is an accumulation point. Every rational number can be an accumulation point modulo ℤ. We determine all accumulation points in [0, 1]. If we fix the value -K2, then the values of pg, pa, mult, embdim and the numerical indices are bounded, while the numbers of the exceptional curves are not bounded.

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