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

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

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.

Low-dimensional Topology and Number Theory

2018 ◽  
Vol 14 (3) ◽  
pp. 2363-2426
Author(s):  
Paul Gunnells ◽  
Walter Neumann ◽  
Adam Sikora ◽  
Don Zagier
Keyword(s):  
Number Theory ◽  
Low Dimensional Topology ◽  
Low Dimensional

Low-Dimensional Topology and Number Theory

2012 ◽  
Vol 9 (3) ◽  
pp. 2541-2596
Author(s):  
Paul Gunnells ◽  
Walter Neumann ◽  
Adam Sikora ◽  
Don Zagier
Keyword(s):  
Number Theory ◽  
Low Dimensional Topology ◽  
Low Dimensional

Low-Dimensional Topology and Number Theory

2021 ◽  
Vol 17 (2) ◽  
pp. 1315-1316
Author(s):  
Paul E. Gunnells ◽  
Thang T. Q. Lê ◽  
Adam S. Sikora ◽  
Don B. Zagier
Keyword(s):  
Number Theory ◽  
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 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
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