The shear free condition is studied for dissipative relativistic self–gravitating fluids in the quasi–static approximation. It is shown that, in the Newtonian limit, such condition implies the linear homology law for the velocity of a fluid element,only if homology conditions are further imposed on the temperature and the emission rate.It is also shown that the shear–free plus the homogeneous e...

We have proposed a complete set of basis Euler operators for updating cell complexes in arbitrary dimensions, which can be classified as homology-preserving and homology-modifying. Here, we define the effect of homology-preserving operators on the incidence graph representation of cell complexes. Based on these operators, we build a multiresolution model for cell complexes represented in the fo...

In this paper, algorithms for computing integer (co)homology of a simplicial complex of any dimension are designed, extending the work done in (7; 9). For doing this, the homology of the object is encoded in an algebraic-topological format (that we call AM-model). Moreover, in the case of 3D binary digital images, having as input AM-models for the images I and J , we design fast algorithms for ...

We construct a stable homotopy refinement of quantum annular homology, link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an $L$ naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum whose cohomology is isomorphic the as modules over $\mathbb{Z}[\mathbb{Z}/r\mathbb{Z}]$. The construction relies on equivariant version Burnside category approach Laws...

We give a new proof of the non-triviality wheel graph homology classes using higher operations on Lie and derived version Koszul duality for modular operads.

Inspired by work of Lipshitz-Sarkar, we show that the module structure on link Floer homology detects split links. Using results Ni, Alishahi-Lipshitz, and establish an analogous detection result for sutured homology.