Let l be an oriented link of d components in a homology 3-sphere. For any nonnegative integer q, let l(q) be the link of d−1 components obtained from l by performing 1/q surgery on its dth component ld. The Mahler measure of the multivariable Alexander polynomial ∆l(q) converges to the Mahler measure of ∆l as q goes to infinity, provided that ld has nonzero linking number with some other compon...

Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We can show that the invariants coincide with signdetermined Reidemeister torsion in a normalized setting and refine the duality theorem. As an application, we obtain stronger necessary co...

Alexander Grothendieck was born in Berlin on 28 March 1928. His father, Sascha Shapiro, an anarchist originally from Russia, took an active part in the revolutionary movements first in Russia, and then in Germany, during the 1920s, where he met Hanka Grothendieck, Alexander’s mother. After the Nazis came to power in Germany it was too dangerous for a Jewish revolutionary to stay there, and the ...

BACKGROUND Randomised controlled trial evidence indicates that Alexander Technique is clinically and cost effective for chronic back pain. The aim of this mixed methods evaluation was to explore the role and perceived impact of Alexander Technique lessons in the naturalistic setting of an acute hospital Pain Management Clinic in England. METHODS To capture changes in health status and resourc...