This paper lays the foundations of a combinatorial homotopy theory, called A-theory, for simplicial complexes, which reflects their connectivity properties. A collection of bigraded groups is constructed, and methods for computation are given. A Seifert-Van Kampen type theorem and a long exact sequence of relative A-groups are derived. A related theory for graphs is constructed as well. This theory provides a general framework encompassing homotopy methods used to prove connectivity results about buildings, graphs, and matroids.

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Healthcare employees were tested for antibodies against SARS-CoV-2. Among 734 employees, the prevalence of SARS-CoV-2 antibodies was 1.6%. Employees with heavy COVID-19 exposure had similar antibody prevalence as those with limited or no exposure. Guidelines for PPE use seem effective for preventing COVID-19 infection in healthcare workers.