Geometric and Topological Aspects of Coxeter Groups and Buildings

  title={Geometric and Topological Aspects of Coxeter Groups and Buildings},
  author={Anne Thomas},
Saddle solutions for the fractional Choquard equation
(−∆)u+ u = (Kα ∗ |u|)|u|u, x ∈ R where s ∈ (0, 1), N ≥ 3 and Kα is the Riesz potential with order α ∈ (0, N). For every Coxeter group G with rank 1 ≤ k ≤ N and p ∈ [2, N+α N−2s ), we construct a
Saddle solutions for the Choquard equation with a general nonlinearity
In the spirit of Berestycki and Lions, we prove the existence of saddle type nodal solutions for the Choquard equation −∆u+ u = ( Iα ∗ F (u) ) F ′(u) in R where N ≥ 2 and Iα is the Riesz potential of
Topological shadows and complexity of islands in multiboundary wormholes
Recently, remarkable progress in recovering the Page curve of an evaporating black hole (BH) in Jackiw-Teitelboim gravity has been achieved through use of Quantum Extremal surfaces (QES).
Coxeter groups, the Davis complex, and isolated flats
Coxter groups arose as a natural generalization of reflection groups. J. Tits defined them in a simple way using generators and relations, that is, using a group presentation W ∼= 〈S | R〉. Coxeter
Quasi-isometric rigidity of a class of right-angled Coxeter groups
We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let $\Gamma_1,\Gamma_2$ be joins of finite generalized thick $m$-gons with $m\geq 3$. We show that the corresponding
Automorphism Groups of Combinatorial Structures
This is a series of lecture notes taken by students during a five lecture series presented by Anne Thomas in 2016 at the MATRIX workshop: The Winter of Disconnectedness.


Buildings, volume 248 of Graduate Texts in Mathematics
  • Theory and applications
  • 2008
Reflection groups and Coxeter groups, volume 29 of Cambridge Studies in Advanced Mathematics
  • 1990
Lectures on Buildings
Reflection Groups And Coxeter Groups
The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
The geometry and topology of Coxeter groups
These notes are intended as an introduction to the theory of Coxeter groups. They closely follow my talk in the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua
The geometry and topology of Coxeter groups, volume 32 of London Mathematical Society Monographs Series
  • 2008
W is finite then there is a point w ∈ W and a spherical subset T ⊆ S
    We will need the following "Cartan-Hadamard Theorem for CAT(0) spaces" due to Gromov: Bibliography
      The "conjugacy problem" for W is decidable. (This question still remains open for the "isomorphism problem
        Σ is a finite-dimensional EW