Automorphic Vector Bundles and Local Systems

2012 ◽  
pp. 91-110
Author(s):  
Jayce Getz ◽  
Mark Goresky
Keyword(s):  
Vector Bundles ◽  
Local Systems

Parabolic Higgs Bundles for Real Reductive Lie Groups

2018 ◽  
pp. 653-680 ◽  
Author(s):  
Ignasi Mundet i Riera
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Lie Group ◽  
Vector Bundles ◽  
Structure Group ◽  
Higgs Bundles ◽  
Local Systems ◽  
Parabolic Structure ◽  
Reductive Lie Groups ◽  
Reductive Lie Group

This chapter explains the correspondence between local systems on a punctured Riemann surface with the structure group being a real reductive Lie group G, and parabolic G-Higgs bundles. The chapter describes the objects involved in this correspondence, taking some time to motivate them by recalling the definitions of G-Higgs bundles without parabolic structure and of parabolic vector bundles. Finally, it explains the relevant polystability condition and the correspondence between local systems and Higgs bundles.

scholarly journals Cohomology jump loci of differential graded Lie algebras

2015 ◽  
Vol 151 (8) ◽  
pp. 1499-1528 ◽  
Author(s):  
Nero Budur ◽  
Botong Wang
Keyword(s):  
Lie Algebras ◽  
Vector Bundles ◽  
Fundamental Groups ◽  
Higgs Bundles ◽  
Infinitesimal Deformation ◽  
Graded Lie Algebras ◽  
Local Systems ◽  
Graded Lie Algebra ◽  
Differential Graded Lie Algebra ◽  
Differential Graded Lie Algebras

To study infinitesimal deformation problems with cohomology constraints, we introduce and study cohomology jump functors for differential graded Lie algebra (DGLA) pairs. We apply this to local systems, vector bundles, Higgs bundles, and representations of fundamental groups. The results obtained describe the analytic germs of the cohomology jump loci inside the corresponding moduli space, extending previous results of Goldman–Millson, Green–Lazarsfeld, Nadel, Simpson, Dimca–Papadima, and of the second author.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

AN INTEGRAL INVOLVING THOMSON'S LOCAL SYSTEMS

1993 ◽  
Vol 19 (1) ◽  
pp. 248 ◽  
Author(s):  
Cai-shi ◽  
Chuan-Song
Keyword(s):  
Local Systems

MONOTONICITY AND LOCAL SYSTEMS

1991 ◽  
Vol 17 (1) ◽  
pp. 291
Author(s):  
Ene
Keyword(s):  
Local Systems

scholarly journals Soil Degradation and Socioeconomic Systems’ Complexity: Uncovering the Latent Nexus

Land ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 30
Author(s):  
Filippo Gambella ◽  
Giovanni Quaranta ◽  
Nathan Morrow ◽  
Renata Vcelakova ◽  
Luca Salvati ◽  
...  
Keyword(s):  
Natural Resource ◽  
Soil Degradation ◽  
Spatial Scales ◽  
Ecological Factors ◽  
Resource Depletion ◽  
Local System ◽  
Local Systems ◽  
Complex Processes ◽  
Socioeconomic Dimension ◽  
External Signals

Understanding Soil Degradation Processes (SDPs) is a fundamental issue for humankind. Soil degradation involves complex processes that are influenced by a multifaceted ensemble of socioeconomic and ecological factors at vastly different spatial scales. Desertification risk (the ultimate outcome of soil degradation, seen as an irreversible process of natural resource destruction) and socioeconomic trends have been recently analyzed assuming “resilience thinking” as an appropriate interpretative paradigm. In a purely socioeconomic dimension, resilience is defined as the ability of a local system to react to external signals and to promote future development. This ability is intrinsically bonded with the socio-ecological dynamics characteristic of environmentally homogeneous districts. However, an evaluation of the relationship between SDPs and socioeconomic resilience in local systems is missing in mainstream literature. Our commentary formulates an exploratory framework for the assessment of soil degradation, intended as a dynamic process of natural resource depletion, and the level of socioeconomic resilience in local systems. Such a framework is intended to provide a suitable background to sustainability science and regional policies at the base of truly resilient local systems.

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