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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Borel conjecture for the torus and the splitting of surgery sets
环面 Borel猜想 外科手术集 分裂
2023/5/10
The Borel conjecture considers the obstruction from homotopy equivalence to homeomorphism for aspherical manifolds. The torus is the first computed case of Borel conjecture with the idea of splitting ...
Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus
Averaging Markov Process Hamiltonian Flow
2015/9/29
We study deterministic and stochastic perturbations of incompressible flows on
a two-dimensional torus. Even in the case of purely deterministic perturbations,
the long-time behavior of such &...
The modular group action on real SL(2){characters of a one-holed torus
one-holed torus group action
2015/9/29
The
action of Γ preserves a Poisson structure de ning a Γ{invariant area form on each
−1(t)\ R3. For t < 2, the action of Γ is properly discontinuous on the four contractible components of &...
Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus
Averaging Markov Process Hamiltonian Flow Gluing Conditions Diffusion on a Graph
2015/9/28
We study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such ...
THE STEINBERG TORUS OF A WEYL GROUP AS A MODULE OVER THE COXETER COMPLEX
Hyperplane arrangement Coxeter complex Steinberg torus
2015/8/14
Associated to each irreducible crystallographic root system , there is a certain
cell complex structure on the torus obtained as the quotient of the ambient space by the
coroot lattice of . This i...
Notation. For a positive integer n and a commutative ring R, we write R[n] to denote R
Z Z[n] =
R[X]=(n), where n denotes the nth cyclotomic polynomial. Thus, for R = Z[n] with n relatively pr...
Unknotting numbers and triple point cancelling numbers of torus-covering knots
Surface knot 2-dimensional braid quandle cocycle invariant unknotting number triple point cancelling number
2012/6/21
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum numb...
Curved noncommutative torus and Gauss--Bonnet
noncommutative torus Gauss--Bonnet Quantum Algebra
2012/4/18
We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac op...
Chern-Simons theory for the noncommutative 3-torus
Chern-Simons theory the noncommutative 3-torus Operator Algebras
2012/4/18
We study the Chern-Simons action, which was defined for noncommutative spaces in general by the author, for the noncommutative 3-torus, the universal C*-algebra generated by 3 unitaries. D. Essouabri,...
The C*-algebra of an affine map on the 3-torus
C*-algebra affine map 3-torus Operator Algebras
2012/4/17
We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is c...
The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus
wavelets lattices multivariate fast Fourier transform periodic multiresolution analysis Dirichlet wavelets
2011/9/21
Abstract: We introduce a fast Fourier Transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a...
Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials
Alexander Polynomial Invariants Chebyshev Polynomials Mathematical Physics
2011/9/22
Abstract: The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. U...
Abstract: The state of a knot is defined in the realm of Chern-Simons topological quantum field theory as a holomorphic section on the SU(2) character manifold of the peripheral torus. We compute the ...
The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus
2D-b-equation diffeomorphism group of the torus geodesic flow sectional curvature Euler equation
2011/9/15
Abstract: We study some geometric aspects of the periodic two-dimensional Camassa-Holm equation (2D-CH) which re-expresses geodesic motion on the diffeomorphism group of the torus $\T = S^1 \times S^1...
SU(N) quantum Racah coefficients & non-torus links
SU(N) quantum Racah coefficients non-torus links High Energy Physics - Theory Mathematical Physics
2011/10/10
Abstract: It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Cher...