(1) π∗(S) −→ π∗(tmf ) −→ MF∗ that we now describe. Both maps are surprisingly close to being isomorphisms (even though π∗(S) and MF∗ have nothing to do with each other). The first map (1) is the Hurewitz homomorphism: being a ring spectrum, tmf admits a unit map from the sphere spectrum S. This induces a map in homotopy π∗(S) → π∗(tmf ), which is an isomorphism on π0. The only torsion in π∗(tmf...

We demonstrate the use of torsion in nanorelays to achieve low voltages, high speeds, single lithography step construction, and a form useful for configurability and electronic design enhancements in three-dimensional integrated implementations. The combined bending and torsion of self-aligned nanopillars facilitates the first top-down fabricated vertical three terminal nanoscale relay. Experim...

We study an invariant of a 3-manifold which consists of Reidemeister torsion for linear representations which pass through a finite group. We show a Dehn surgery formula on this invariant and compute that of a Seifert manifold over S 2. As a consequence we obtain a necessary condition for a result of Dehn surgery along a knot to be Seifert fibered, which can be applied even in a case where abel...

A. The aim of this paper is to give an explicit formula for the SL 2(C)-twisted Reidemeister torsion in the case of twist knots. For hyperbolic twist knots, we also prove that the twisted Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot. Tables giving approximations of the twisted Reidemeister torsion for ...

We study two sorts of actions on the space of conjugacy classes of irreducible S U2representations of a knot group. One of them is an involution which comes from the algebraic structure of S U2 and the other is the action by the outer automorphism group of the knot group. In particular, we consider them on a 1-dimensional smooth part of the space, which is canonically oriented and metrized via ...

BACKGROUND Acute scrotal pain is a common urological emergency. Urgent exploration is the standard means of management, as no investigation can confidently exclude torsion of testis from the differential diagnoses. In our department, all patients up to the age of 40 years, presenting with acute scrotal pain undergo emergency scrotal exploration. AIM This study assesses the outcome of such a p...

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...

We present a novel method to simulate bending and torsion of elastic rods within the position-based dynamics (PBD) framework. The main challenge is that torsion effects of Cosserat rods are described in terms of material frames which are attached to the centerline of the rod. But frames or orientations do not fit into the classical position-based dynamics formulation. To solve this problem we i...

Torsion appears due to fermions coupled to gravity and leads to the strongest particle physics bounds on flat extra dimensions. In this work, we consider torsion constraints in the case of a warped extra dimension with brane and bulk fermions. From current data we obtain a 3σ bound on the TeV–brane mass scale Λπ ≥ 2.2 (10) TeV for the AdS curvature k = 1 (0.01) in (reduced) Planck units. If Dir...

For the alternating group A6 of degree 6, Zassenhaus’ conjecture about rational conjugacy of torsion units in integral group rings is confirmed.