arXiv subjects
Publications and source records attributed to Serge Vlăduţ.
This note corrects the paper \cite{ex}, where lattice sequences having exponentially large kissing numbers were constructed. However it was noted in \cite{dif} that the arguments in that paper are not sufficient. Here we correct the construction which leads to similar results, albeit with much smaller constants.
We show that the lattice Hadwiger number of superballs is exponential in the dimension. The same is true for some more general convex bodies.
We construct a sequence of lattices $\{L_{n_i}\subset \mathbb R^{n_i}\}$ for $n_i\longrightarrow\infty$, with exponentially large kissing numbers, namely, $\log_2τ(L_{n_i})> 0.0338\cdot n_i -o(n_i)$. We also show that the maximum lattice kissing number $ τ^l_{n}$ in $n$ dimensions verifies $\log_2τ^l_{n}> 0.0219\cdot n -o(n)$.
For $G$ a finite group, we prove in dimension 2 that there is a monoidal equivalence between the category of $G$-equivariant topological quantum field theories and the category of $G$-Frobenius algebras, this was proved by G. Moore and G. Segal. This work consists to give, in more detail, a proof of this result.