A formula for the generalized Sato-Levine invariant

Abstract

The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.

A Simple Formula for the Casson–walker Invariant

“…Figure 13. The behavior of λ w (M t ) and its approximation (dotted graph) for H (2,3,2) The following theorem shows the power series presentation of λ w (M t ). Then for |t| > |n| √ |a0b0| we have…”

“…Once the invariance of U (L) is established, one can identify it with the generalized [2,3,9,13]), where c k is the coefficient at z k of the Conway polynomial. There are several ways to do that.…”

“…We show that their results extend to the case of arbitrary integer framings and provide a simple Gauss diagram formula in this general case. The main ingredient of this formula appeared first in [16] and is now known as the generalized Sato-Levine invariant, see [2,3,9,13]. The Gauss diagram formula enables us to calculate the values of λ w (M L ) in a simple and straightforward way starting from any diagram of a 2-component link.…”

Self C2-equivalence of two-component links and invariants of link maps

“…Hence Λ is self C 2 -equivalent to a string linkΛ =Λ + Λ − such thatΛ − is unknotted. Let g be a 1 2 -quasi-isotopy between Λ andΛ , and let 1Λ be the identical self-homotopy ofΛ . Then h := h * g * 1Λ is a link homotopy between Λ andΛ .…”

“…To this end, we grow a "tendril", which is eliminated after the delayed intersection is finally performed. The author learned this technique from P. Akhmetiev; the word "tendril" is also his (see [1]).…”