scholarly journals Seiberg–Witten Floer Homotopy Contact Invariant

2021 ◽  
Vol 58 (4) ◽  
pp. 505-558

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer–Mrowka–Ozsváth–Szabó. Moreover, we prove a gluing formula relating our invariant with the first author’s Bauer–Furuta type invariant, which refines Kronheimer–Mrowka’s invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.

2021 ◽  
Vol 11 (2) ◽  
pp. 779
Author(s):  
Dimitrios Dardalis ◽  
Amiyo Basu ◽  
Matt J. Hall ◽  
Ronald D. Mattthews

The Rotating Liner Engine (RLE) concept is a design concept for internal combustion engines, where the cylinder liner rotates at a surface speed of 2–4 m/s in order to assist piston ring lubrication. Specifically, we have evidence from prior art and from our own research that the above rotation has the potential to eliminate the metal-to-metal contact/boundary friction that exists close to the piston reversal areas. This frictional source becomes a significant energy loss, especially in the compression/expansion part of the cycle, when the gas pressure that loads the piston rings and skirts is high. This paper describes the Diesel RLE prototype constructed from a Cummins 4BT and the preliminary observations from initial low load testing. The critical technical challenge, namely the rotating liner face seal, appears to be operating with negligible gas leakage and within the hydrodynamic lubrication regime for the loads tested (peak cylinder pressures of the order of 100 bar) and up to about 10 bar BMEP (brake mean effective pressure). Preliminary testing has proven that the metal-to-metal contact in the piston assembly mostly vanished, and a friction reduction at idle conditions of about 40% as extrapolated to a complete engine has taken place. It is expected that as the speed increases, the friction reduction percentage will diminish, but as the load increases, the friction reduction will increase. The fuel economy benefit over the US Heavy-Duty driving cycle will likely be of the order of 10% compared to a standard engine.


1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]


2014 ◽  
Vol 17 (5) ◽  
Author(s):  
John R. Britnell ◽  
Mark Wildon

AbstractIt is known that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general captures more information; using this invariant the result on centralizers is extended to arbitrary fields. The converse is also proved: thus two matrices have conjugate centralizers if and only if they have the same generalized type. The paper ends with the analogous results for symmetric and alternating groups.


2009 ◽  
Vol 18 (06) ◽  
pp. 825-840 ◽  
Author(s):  
J. JUYUMAYA ◽  
S. LAMBROPOULOU

In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the Yokonuma–Hecke algebras Y d,n(u) and the theory of singular braids. The Yokonuma–Hecke algebras have a natural topological interpretation in the context of framed knots. Yet, we show that there is a homomorphism of the singular braid monoid SBn into the algebra Y d,n(u). Surprisingly, the trace does not normalize directly to yield a singular link invariant, so a condition must be imposed on the trace variables. Assuming this condition, the invariant satisfies a skein relation involving singular crossings, which arises from a quadratic relation in the algebra Y d,n(u).


Proceedings ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 24
Author(s):  
Klaus Kirsten ◽  
Yoonweon Lee
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document