arXiv subjects

Erica Minuz

Publications and source records attributed to Erica Minuz.

2 recordsLinked to original sources

arXiv2020

Graph cohomologies and rational homotopy type of configuration spaces

We compare the cohomology complex defined by Baranovsky and Sazdanović, that is the $E_{1}$ page of a spectral sequence converging to the homology of the configuration space depending on a graph, with the rational model for the configuration space given by Kriz and Totaro. In particular we generalize the rational model to any graph and to an algebra over any field. We show that, in the case of configuration spaces of point on a even dimensional manifold, the dual of the Baranovsky and Sazdanović's complex is quasi equivalent to this generalized version of the Kriz's model.

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arXiv2020

Cohomology of generalised configuration spaces of points on $\mathbb{R}^r$

We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and Cohen. However, our computations give a generalisation to any graph and an alternative proof of the classical result. Moreover, we show that there are deletion-contraction short exact sequences for this cohomology rings.

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