On equivariant embeddings of generalized Baumslag–Solitar groups

Equivariant Dierential Embeddings

Equivariant differential embeddings

Takens Dynamical Systems and Turbulence, Lecture Notes in Mathematics, edited by D. A. Rand and L. S. Young Springer-Verlag, New York, 1981 , Vol. 898, pp. 366–381 has shown that a dynamical system may be reconstructed from scalar data taken along some trajectory of the system. A reconstruction is considered successful if it produces a system diffeomorphic to the original. However, if the origi...

Topology of Spaces of Equivariant Symplectic Embeddings

We compute the homotopy type of the space of Tn-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic–toric manifold (M, σ), and use this computation to define a Z≥0-valued step function on R≥0 which is an invariant of the symplectic–toric type of (M, σ). We conclude with a discussion of the partially equivariant case of th...

Equivariant Embeddings of Trees into Hyperbolic Spaces

For every cardinal α ≥ 2 there are three complete constant curvature model manifolds of Hilbert dimension α: the sphere S, the Euclidean space E and the hyperbolic space H. Studying isometric actions on these spaces corresponds in the first case to studying orthogonal representations and in the second case to studying cohomology in degree one with orthogonal representations as coefficients. In ...

On the eigenvalues of Cayley graphs on generalized dihedral groups

‎Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$‎. ‎Then the energy of‎ ‎$Gamma$‎, ‎a concept defined in 1978 by Gutman‎, ‎is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$‎. ‎Also‎ ‎the Estrada index of $Gamma$‎, ‎which is defined in 2000 by Ernesto Estrada‎, ‎is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$‎. ‎In this paper‎, ‎we compute the eigen...