  Recently a generic class of three-dimensional band structures was identified
that host two-fold line degeneracies meeting at three-fold or triple point
degeneracies, which resist the usual topological characterization of isolated
point degeneracies as in Dirac/Weyl semimetals. For these so-called ``Nexus"
fermions which lie beyond Dirac/Weyl fermions, we lay out several concepts to
characterize the wavefunction geometry and spell out its topology. Our approach
is based on an understanding of the analyticity properties of Nexus
wavefunctions building on a two-dimensional analogue studied recently by us. We
use this to write down a homological classification of various Nexus triple
point degeneracies in three dimensions.
