Concordance of Bing doubles and boundary genus

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature $\sigma$, then the n-iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than $2^{n-1}\sigma$. The same result holds with $\sigma$ replaced by $2\tau$, twice the Ozsvath-Szabo knot concordance invariant.Comment: 13 pages, 7 figure

On the nonorientable 4-genus of double twist knots

We investigate the nonorientable 4-genus $\gamma_4$ of a special family of 2-bridge knots, the twist knots and double twist knots $C(m,n)$. Because the nonorientable 4-genus is bounded by the nonorientable 3-genus, it is known that $\gamma_4(C(m,n)) \le 3$. By using explicit constructions to obtain upper bounds on $\gamma_4$ and known obstructions derived from Donaldson's diagonalization theorem to obtain lower bounds on $\gamma_4$, we produce infinite subfamilies of $C(m,n)$ where $\gamma_4=0,1,2,$ and $3$, respectively. However, there remain infinitely many double twist knots where our work only shows that $\gamma_4$ lies in one of the sets $\{1,2\}, \{2,3\}$, or $\{1,2,3\}$. We tabulate our results for all $C(m,n)$ with $|m|$ and $|n|$ up to 50. We also provide an infinite number of examples which answer a conjecture of Murakami and Yasuhara.Comment: Some exposition is revised, a figure is added, and typos are corrected, following comments from the refere

Synthesis of a 3D network of Pt nanowires by atomic layer deposition on carbonaceous template

The formation of a 3D network composed of free standing and interconnected Pt nanowires is achieved by a two-step method, consisting of conformal deposition of Pt by atomic layer deposition (ALD) on a forest of carbon nanotubes and subsequent removal of the carbonaceous template. Detailed characterization of this novel 3D nanostructure was carried out by transmission electron microscopy (TEM) and electrochemical impedance spectroscopy (EIS). These characterizations showed that this pure 3D nanostructure of platinum is self-supported and offers an enhancement of the electrochemically active surface area by a factor of 50