Feynman Diagrams and Low-Dimensional Topology

1994 ◽  
pp. 97-121 ◽  
Author(s):  
Maxim Kontsevich
Keyword(s):  
Feynman Diagrams ◽  
Low Dimensional Topology ◽  
Low Dimensional

Geometry and Physics: Volume II

2018 ◽  
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Geometric Analysis ◽  
Mathematical Physics ◽  
Poisson Geometry ◽  
Special Holonomy ◽  
Low Dimensional Topology ◽  
Generalized Complex Structures ◽  
Wide Range ◽  
Low Dimensional

These volumes contain the proceedings of the conference held at Aarhus, Oxford and Madrid in September 2016 to mark the seventieth birthday of Nigel Hitchin, one of the world’s foremost geometers and Savilian Professor of Geometry at Oxford. The proceedings contain twenty-nine articles, including three by Fields medallists (Donaldson, Mori and Yau). The articles cover a wide range of topics in geometry and mathematical physics, including the following: Riemannian geometry, geometric analysis, special holonomy, integrable systems, dynamical systems, generalized complex structures, symplectic and Poisson geometry, low-dimensional topology, algebraic geometry, moduli spaces, Higgs bundles, geometric Langlands programme, mirror symmetry and string theory. These volumes will be of interest to researchers and graduate students both in geometry and mathematical physics.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

Low-Dimensional Topology and Number Theory

2010 ◽  
pp. 2101-2163 ◽  
Author(s):  
Paul Gunnells ◽  
Walter Neumann ◽  
Adam Sikora ◽  
Don Zagier
Keyword(s):  
Number Theory ◽  
Low Dimensional Topology ◽  
Low Dimensional

scholarly journals Cross-sections of unknotted ribbon disks and algebraic curves

2019 ◽  
Vol 155 (2) ◽  
pp. 413-423
Author(s):  
Kyle Hayden
Keyword(s):  
Cross Sections ◽  
Algebraic Curves ◽  
American Mathematical Society ◽  
Geometric Topology ◽  
Mathematical Society ◽  
Advanced Mathematics ◽  
Low Dimensional Topology ◽  
Low Dimensional ◽  
Holomorphic Disks

We resolve parts (A) and (B) of Problem 1.100 from Kirby’s list [Problems in low-dimensional topology, in Geometric topology, AMS/IP Studies in Advanced Mathematics, vol. 2 (American Mathematical Society, Providence, RI, 1997), 35–473] by showing that many nontrivial links arise as cross-sections of unknotted holomorphic disks in the four-ball. The techniques can be used to produce unknotted ribbon surfaces with prescribed cross-sections, including unknotted Lagrangian disks with nontrivial cross-sections.

scholarly journals Algebraic Structures in Low-Dimensional Topology

2014 ◽  
Vol 11 (2) ◽  
pp. 1403-1458 ◽  
Author(s):  
Louis Kauffman ◽  
Vassily Manturov ◽  
Kent Orr ◽  
Robert Schneiderman
Keyword(s):  
Algebraic Structures ◽  
Low Dimensional Topology ◽  
Low Dimensional

Low-dimensional Topology and Number Theory

2014 ◽  
Vol 11 (3) ◽  
pp. 2115-2176
Author(s):  
Paul Gunnells ◽  
Walter Neumann ◽  
Adam Sikora ◽  
Don Zagier
Keyword(s):  
Number Theory ◽  
Low Dimensional Topology ◽  
Low Dimensional

Parametrizing Fuchsian Subgroups of the Bianchi Groups

1991 ◽  
Vol 43 (1) ◽  
pp. 158-181 ◽  
Author(s):  
C. Maclachlan ◽  
A. W. Reid
Keyword(s):  
Number Theory ◽  
Group Theory ◽  
Present Article ◽  
Ring Of Integers ◽  
Low Dimensional Topology ◽  
Low Dimensional

Let dbe a positive square-free integer and let Od denote the ring of integers in . The groups PSL2(Od) are collectively known as the Bianchi groups and have been widely studied from the viewpoints of group theory, number theory and low-dimensional topology. The interest of the present article is in geometric Fuchsian subgroups of the groups PSL2(Od). Clearly PSL2 is such a subgroup; however results of [18], [19] show that the Bianchi groups are rich in Fuchsian subgroups.

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