scholarly journals Expansive flows of the three-sphere

2015 ◽  
Vol 41 ◽  
pp. 91-101 ◽  
Author(s):  
Alfonso Artigue
Keyword(s):  
Three Sphere ◽  
Expansive Flows

scholarly journals Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Stefano Baiguera ◽  
Troels Harmark ◽  
Nico Wintergerst
Keyword(s):  
Classical Limit ◽  
Particle Number ◽  
Matrix Theory ◽  
Companion Paper ◽  
Positive Definite ◽  
Normal Ordering ◽  
Yang Mills ◽  
Three Sphere ◽  
Dilatation Operator ◽  
Definite Expressions

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

Involutions With Two Fixed Points on the Three-Sphere

1963 ◽  
Vol 78 (3) ◽  
pp. 582 ◽  
Author(s):  
G. R. Livesay
Keyword(s):  
Fixed Points ◽  
Three Sphere

STRUCTURED GROUPS AND LINK-HOMOTOPY

1993 ◽  
Vol 02 (01) ◽  
pp. 37-63 ◽  
Author(s):  
JAMES R. HUGHES
Keyword(s):  
Automorphism Groups ◽  
Original Version ◽  
Theoretic Approach ◽  
Homotopy Classes ◽  
Structure Preserving ◽  
Three Sphere ◽  
Complex Program ◽  
Link Homotopy ◽  
Structured Groups

We study link-homotopy classes of links in the three sphere using reduced groups endowed with peripheral structures derived from meridian-longitude pairs. Two types of peripheral structures are considered — Milnor’s original version (called “pre-peripheral structures” in Levine’s terminology) and Levine’s refinement (called simply “peripheral structures”). We show here that pre-peripheral structures are not strong enough to classify links up to link-homotopy, and that Levine’s peripheral structures, although strong enough to distinguish those classes not distinguished by pre-peripheral structures, are also in all likelihood not strong enough to distinguish all link-homotopy classes. Following Levine’s classification program, we compare structure-preserving and realizable automorphisms, using an obstruction-theoretic approach suggested by work of Habegger and Lin. We find that these automorphism groups are in general different, so that a more complex program for classification by structured groups is required.

Optimal motion control of three-sphere based low-Reynolds number swimming microrobot

Robotica ◽  
2021 ◽  
pp. 1-17
Author(s):  
Hossein Nejat Pishkenari ◽  
Matin Mohebalhojeh
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Optimal Controller ◽  
Optimal Motion ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Three Sphere ◽  
Low Reynolds Number Swimming ◽  
Number Flow ◽  
Low Reynolds

Abstract Microrobots with their promising applications are attracting a lot of attention currently. A microrobot with a triangular mechanism was previously proposed by scientists to overcome the motion limitations in a low-Reynolds number flow; however, the control of this swimmer for performing desired manoeuvres has not been studied yet. Here, we have proposed some strategies for controlling its position. Considering the constraints on arm lengths, we proposed an optimal controller based on quadratic programming. The simulation results demonstrate that the proposed optimal controller can steer the microrobot along the desired trajectory as well as minimize fluctuations of the actuators length.

Consensus and balancing on the three-sphere

2018 ◽  
Vol 76 (3) ◽  
pp. 575-586 ◽  
Author(s):  
Aladin Crnkić ◽  
Vladimir Jaćimović
Keyword(s):  
Three Sphere

scholarly journals A splicing formula for the LMO invariant

2020 ◽  
pp. 1-28
Author(s):  
Gwénaël Massuyeau ◽  
Delphine Moussard
Keyword(s):  
Finite Type ◽  
Rational Homology ◽  
Three Sphere ◽  
Type Invariant ◽  
Low Degrees ◽  
Surgery Formula

Abstract We prove a “splicing formula” for the LMO invariant, which is the universal finite-type invariant of rational homology three-spheres. Specifically, if a rational homology three-sphere M is obtained by gluing the exteriors of two framed knots $K_1 \subset M_1$ and $K_2\subset M_2$ in rational homology three-spheres, our formula expresses the LMO invariant of M in terms of the Kontsevich–LMO invariants of $(M_1,K_1)$ and $(M_2,K_2)$ . The proof uses the techniques that Bar-Natan and Lawrence developed to obtain a rational surgery formula for the LMO invariant. In low degrees, we recover Fujita’s formula for the Casson–Walker invariant, and we observe that the second term of the Ohtsuki series is not additive under “standard” splicing. The splicing formula also works when each $M_i$ comes with a link $L_i$ in addition to the knot $K_i$ , hence we get a “satellite formula” for the Kontsevich–LMO invariant.

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