Academic literature on the topic 'Cup product bundle gerbe'

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. If (L → M → N) is a Lie 2-crossed module and Y → X is a surjective submersion then an (L → M → N)-bundle 2-gerbe over X is defined in terms of a so-called (L → M → N)-bundle gerbe over the fiber product Y[2] = Y × XY, which is an (L → M)-bundle gerbe over Y[2] equipped with a trivialization under the change of its structure crossed module from L → M to 1 → N, and which is subjected to further conditions on higher fiber products Y[3], Y[4] and Y[5]. String structures can be described and classified using 2-crossed module bundle 2-gerbes.

AbstractIn this paper we study the Chen–Ruan cohomology ring of weighted projective spaces. Given a weighted projective space we determine all of its twisted sectors and the corresponding degree shifting numbers. The main result of this paper is that the obstruction bundle over any 3-multisector is a direct sum of line bundles which we use to compute the orbifold cup product. Finally we compute the Chen–Ruan cohomology ring of weighted projective space

Let [Formula: see text] be the fundamental group of a sapphire that admits the Sol geometry and is not a torus bundle. We determine a finite free resolution of [Formula: see text] over [Formula: see text] and calculate a partial diagonal approximation for this resolution. We also compute the cohomology rings [Formula: see text] for [Formula: see text] and [Formula: see text] for an odd prime [Formula: see text], and indicate how to compute the groups [Formula: see text] and the multiplicative structure given by the cup product for any system of coefficients [Formula: see text].

This thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous applications in physics.
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2019

Abstract Pneumatic Systems, especially those working with compressed air, come with several drawbacks like poor energy efficiency, high level of emission and limited digitalization amongst others. Therefore, there are efforts in industry to replace pneumatics with purely electrical systems. A promising approach in gripping and handling technology is the shape memory alloy (SMA)-based vacuum suction cup, which was first presented at the 2018 SMASIS conference [1]. The working principle relies on an antagonistic SMA-based actuator system in combination with a bistable spring and a silicone membrane. This paper presents the structure and further development of the vacuum suction cup, whose vacuum generation is independent of a temporary or stable airflow. The focus lies on the improvement of the existing mechanics to a more maintenance-friendly design on route to a commercial product. For the implementation new SMA-bundles are created and the wire guides are adjusted accordingly. Besides, several experiments and analyses are carried out to validate the behavior of the mechanics with the new setup using the self-sensing effect. These investigations focus on the effects of varying bundle lengths, lever arms, and damaged bundles on performance. It is shown that the new design approach offers easier handling and robustness in the event of an actuator break.