Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

Sarcoid-like reaction in a patient recovering from coronavirus disease 19 pneumonia

As coronavirus disease 2019 (COVID-19) cases continue to increase, so do the reported extrapulmonary manifestations of this disease. To date, described dermatologic manifestations of COVID-19 include pernio-like acral nodules, dengue fever–like petechiae, vesiculobullous eruptions, pityriasis rosea and viral-like exanthems, retiform purpura, and livedo reticularis.1 We describe a patient with new-onset, biopsy confirmed sarcoid-like reaction in the setting of COVID-19 pneumonia and postulate a role for this immunologic reaction in hastening disease recovery