ترغب بنشر مسار تعليمي؟ اضغط هنا

Links with splitting number one

188   0   0.0 ( 0 )
 نشر من قبل Marc Lackenby
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Marc Lackenby




اسأل ChatGPT حول البحث

We provide an algorithm to determine whether a link L admits a crossing change that turns it into a split link, under some fairly mild hypotheses on L. The algorithm also provides a complete list of all such crossing changes. It can therefore also determine whether the unlinking number of L is 1.



قيم البحث

اقرأ أيضاً

159 - Michael J. Williams 2009
It is shown that if the exterior of a link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.
In the 1980s Daryl Cooper introduced the notion of a C-complex (or clasp-complex) bounded by a link and explained how to compute signatures and polynomial invariants using a C-complex. Since then this was extended by works of Cimasoni, Florens, Mello r, Melvin, Conway, Toffoli, Friedl, and others to compute other link invariants. Informally a C-complex is a union of surfaces which are allowed to intersect each other in clasps. The purpose of the current paper is to study the minimal number of clasps amongst all C-complexes bounded by a fixed link $L$. This measure of complexity is related to the number of crossing changes needed to reduce $L$ to a boundary link. We prove that if $L$ is a 2-component link with nonzero linking number, then the linking number determines the minimal number of clasps amongst all C-complexes. In the case of 3-component links, the triple linking number provides an additional lower bound on the number of clasps in a C-complex.
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic technique, combined with Ozsvath, Stipsicz, and Szabos Upsilon invarian t, allows us to determine the exact cobordism distance between torus knots with braid index two and six.
115 - Michael J. Williams 2009
A knot k in a closed orientable 3-manifold is called nonsimple if the exterior of k possesses a properly embedded essential surface of nonnegative Euler characteristic. We show that if k is a nonsimple prime tunnel number one knot in a lens space M ( where M does not contain any embedded Klein bottles), then k is a (1,1) knot. Elements of the proof include handle addition and Dehn filling results/techniques of Jaco, Eudave-Munoz and Gordon as well as structure results of Schultens on the Heegaard splittings of graph manifolds.
The Thurston norm of a 3-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of 3-manifolds $M$ with $b_1(M) = 2$, and whose fundamental groups admit presentat ions with two generators and one relator. We show that even among this special class, there are 3-manifolds such that the unit ball of the Thurston norm has arbitrarily many faces.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا