代数拓扑/一般拓扑/几何拓扑学术速递[1.10]
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math.AT代数拓扑，共计5篇
math.GN一般拓扑，共计0篇
math.GT几何拓扑，共计1篇
1.math.AT代数拓扑:
【1】 Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
标题：导出交织距离的完备性与非光滑物体的束量化
链接：https://arxiv.org/abs/2201.02598
备注：33 pages, 1 figure, comments are welcome
摘要：We investigate sheaf-theoretic methods to deal with non-smooth objects in
symplectic geometry. We show the completeness of a derived category of sheaves
with respect to the interleaving-like distance and construct a sheaf
quantization of a hameomorphism. We also develop Lusternik-Schnirelmann theory
in the microlocal theory of sheaves. With these new tools, we prove an
Arnold-type theorem for the image of the zero-section under a hameomorphism by
a purely sheaf-theoretic method.
【2】 The Persistence Landscapes of Affine Fractals
标题：仿射分形的持久景观
链接：https://arxiv.org/abs/2201.02552
备注：32 pages, 5 figures. Comments welcome
摘要：We develop a method for calculating the persistence landscapes of affine
fractals using the parameters of the corresponding transformations. Given an
iterated function system of affine transformations that satisfies a certain
compatibility condition, we prove that there exists an affine transformation
acting on the space of persistence landscapes which intertwines the action of
the iterated function system. This latter affine transformation is a strict
contraction and its unique fixed point is the persistence landscape of the
affine fractal. We present several examples of the theory as well as confirm
the main results through simulations.
【3】 The automorphism groups of Artin groups of edge-separated CLTTF graphs
标题：边分离CLTTF图的Artin群的自同构群
链接：https://arxiv.org/abs/2201.02502
备注：30 pages, 6 figures
摘要：We provide an explicit presentation of the automorphism group of an
edge-separated CLTTF Artin group.
【4】 Diffeomorphisms of discs
标题：圆盘的微分同态
链接：https://arxiv.org/abs/2201.02380
备注：Contributed to the Proceedings of the 2022 ICM
摘要：I describe what is currently known, for $d \geq 5$, about the rational
homotopy type of the group of diffeomorphisms of the $d$-disc relative to its
boundary, and the closely related group of homeomorphisms of $d$-dimensional
Euclidean space.
【5】 Persistent Homology for Breast Tumor Classification using Mammogram Scans
标题：使用乳腺X线扫描实现乳腺肿瘤分类的持久同源性
链接：https://arxiv.org/abs/2201.02295
备注：10 pages
摘要：An Important tool in the field topological data analysis is known as
persistent Homology (PH) which is used to encode abstract representation of the
homology of data at different resolutions in the form of persistence diagram
(PD). In this work we build more than one PD representation of a single image
based on a landmark selection method, known as local binary patterns, that
encode different types of local textures from images. We employed different PD
vectorizations using persistence landscapes, persistence images, persistence
binning (Betti Curve) and statistics. We tested the effectiveness of proposed
landmark based PH on two publicly available breast abnormality detection
datasets using mammogram scans. Sensitivity of landmark based PH obtained is
over 90% in both datasets for the detection of abnormal breast scans. Finally,
experimental results give new insights on using different types of PD
vectorizations which help in utilising PH in conjunction with machine learning
classifiers.
2.math.GN一般拓扑:
3.math.GT几何拓扑:
【1】 Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
标题：无限图的纯映射类群的粗几何
链接：https://arxiv.org/abs/2201.02559
备注：41 pages, 10 figures
摘要：We discuss the large-scale geometry of pure mapping class groups of locally
finite, infinite graphs, motivated from recent work by Algom-Kfir--Bestvina and
the work of Mann--Rafi on the large-scale geometry of mapping class groups of
infinite-type surfaces. Using the framework of Rosendal for coarse geometry of
non-locally compact groups, we classify when the pure mapping class group of a
locally finite, infinite graph is globally coarsely bounded (an analog of
compact) and when it is locally coarsely bounded (an analog of locally
compact). Our techniques also give lower bounds on the first integral
cohomology of the pure mapping class group for some graphs and show that some
of these groups have continuous actions on simplicial trees.
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