ترغب بنشر مسار تعليمي؟ اضغط هنا

Relative Q-gradings from bordered Floer theory

298   0   0.0 ( 0 )
 نشر من قبل Robert Lipshitz
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we show how to recover the relative Q-grading in Heegaard Floer homology from the noncommutative grading on bordered Floer homology.



قيم البحث

اقرأ أيضاً

This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard Floer homology can be used for computations.
We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two differe
We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrized boundary. This paper is meant to serve as a gentle int roduction to the subject, and does not itself have immediate topological applications.
We describe a weighted $A_infty$-algebra associated to the torus. We give a combinatorial construction of this algebra, and an abstract characterization. The abstract characterization also gives a relationship between our algebra and the wrapped Fuka ya category of the torus. These algebras underpin the (unspecialized) bordered Heegaard Floer homology for three-manifolds with torus boundary, which will be constructed in forthcoming work.
We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold $Y$, with minimal conditions on the bordered-sutured structure, satisfies an unoriented skein exact triangle. This generalizes a theorem by Man olescu for links in $S^3$. We give a theoretical proof of this result by adapting holomorphic polygon counts to the bordered-sutured setting, and also give a combinatorial description of all maps involved and explicitly compute them. We then show that, for $Y = S^3$, our exact triangle coincides with Manolescus. Finally, we provide a graded version of our result, explaining in detail the grading reduction process involved.
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