An Explicit View of the Hitchin Fibration on the Betti Side for ℙ1 minus Five Points

2018 ◽  
pp. 705-724
Author(s):  
Carlos T. Simpson
Keyword(s):  
Conjugacy Classes ◽  
Character Variety ◽  
Tubular Neighbourhood ◽  
Local Systems ◽  
Hitchin Fibration ◽  
Dual Complex

The dual complex of the divisor at infinity of the character variety of local systems on P1−{t1,…,t5} with monodromies in prescribed conjugacy classes Ci⊂SL2(C), was shown by Komyo to be the sphere S3. This chapter compares in some detail the projection from a tubular neighbourhood to this dual complex, with the corresponding Hitchin fibration at infinity.

scholarly journals Traceless SU(2) representations of 2-stranded tangles

2016 ◽  
Vol 162 (1) ◽  
pp. 101-129 ◽  
Author(s):  
YOSHIHIRO FUKUMOTO ◽  
PAUL KIRK ◽  
JUANITA PINZÓN-CAICEDO
Keyword(s):  
Conjugacy Classes ◽  
Character Variety ◽  
Restriction Map ◽  
Pretzel Knots ◽  
Non Linear

AbstractGiven a 2-stranded tangle T contained in a ℤ-homology ball Y, we investigate the character variety R(Y, T) of conjugacy classes of traceless SU(2) representations of π1(Y \ T). In particular we completely determine the subspace of binary dihedral representations, and identify all of R(Y, T) for many tangles naturally associated to knots in S3. Moreover, we determine the image of the restriction map from R(T, Y) to the traceless SU(2) character variety of the 4-punctured 2-sphere (the pillowcase). We give examples to show this image can be non-linear in general, and show it is linear for tangles associated to pretzel knots.

scholarly journals Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points

2014 ◽  
Vol 25 (14) ◽  
pp. 1450125 ◽  
Author(s):  
Marina Logares ◽  
Vicente Muñoz
Keyword(s):  
Elliptic Curve ◽  
Moduli Space ◽  
Betti Numbers ◽  
Conjugacy Classes ◽  
Character Variety ◽  
Higgs Bundles ◽  
Hodge Numbers ◽  
Hodge Polynomials ◽  
Marked Points

We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

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.

scholarly journals Persistent local systems

2021 ◽  
Vol 386 ◽  
pp. 107795
Author(s):  
Robert MacPherson ◽  
Amit Patel
Keyword(s):  
Local Systems

scholarly journals Groups with boundedly finite conjugacy classes of commutators

2018 ◽  
Vol 69 (3) ◽  
pp. 1047-1051 ◽  
Author(s):  
Gláucia Dierings ◽  
Pavel Shumyatsky
Keyword(s):  
Conjugacy Classes ◽  
Finite Conjugacy
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