关于ALE向量束的刚性

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-01-16 DOI:10.1016/j.topol.2025.109217

Fatemeh Asadi , Zohreh Fathi , Sajjad Lakzian

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引用次数: 0

摘要

讨论了秩≥2的渐近圆锥（AC）总空间具有充分连通链路的向量束的拓扑刚性。我们的重点将主要放在ALE（渐近局部欧几里德）束上。在光滑范畴内，我们通过证明只有S2、RP2和开可缩流形允许ALE切束，对所有ALE切束进行了拓扑分类。我们还讨论其他有趣的啤酒向量的拓扑和几何刚度包。

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On rigidity of ALE vector bundles

We discuss the topological rigidity of vector bundles with asymptotically conical (AC) total spaces of rank ≥2 with a sufficiently connected link. Our focus will mainly be on ALE (asymptotically locally Euclidean) bundles. Within the smooth category, we topologically classify all ALE tangent bundles by showing that only

S^{2}

{RP}^{2}

and open contractible manifolds admit ALE tangent bundles. We also discuss other interesting topological and geometric rigidities of ALE vector bundles.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.