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We consider a deformation of the Robert-Wagner foam evaluation formula, with an eye toward a relation to formal groups. Integrality of the deformed evaluation is established, giving rise to state spaces for planar GL(N) MOY graphs (Murakami-Ohtsuki-Yamada graphs). Skein relations for the deformation are worked out in details in the GL(2) case. These skein relations deform GL(2) foam relations of Beliakova, Hogancamp, Putyra and Wehrli. We establish the Reidemeister move invariance of the resulting chain complexes assigned to link diagrams, giving us a link homology theory.
In this paper we introduce a chain complex $C_{1 pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of resolution
We show that if a prime homology sphere has the same Floer homology as the standard three-sphere, it does not contain any incompressible tori.
In this paper, we study the higher Hochschild functor and its relationship with factorization algebras and topological chiral homology. To this end, we emphasize that the higher Hochschild complex is a $(infty,1)$-functor from the category $hsset tim
We define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular links. Besides the consistency of its definition, we prove that this homo
The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with an emphasis on the local equivalence methods coming from Pin(2)- equivari