  In this work we investigate the Swampland Cobordism Conjecture in the context
of type IIB string theory geometries with non-trivial duality bundle. Quite
remarkably, we find that many non-trivial bordism classes with duality bundles
in Mp$(2,\mathbb{Z})$, a double cover of SL$(2,\mathbb{Z})$ related to
fermions, correspond to asymptotic boundaries of well-known supersymmetric
F-theory backgrounds. These include $[p,q]$-7-branes, non-Higgsable clusters,
S-folds, as well as various lower-dimensional generalizations. These string
theoretic objects break the global symmetries associated to the non-trivial
bordism groups, providing a strong test of the Cobordism Conjecture. Further
including worldsheet orientation reversal promotes the duality group to the
Pin$^+$ cover of GL$(2,\mathbb{Z})$. The corresponding bordism groups require a
new non-supersymmetric "reflection 7-brane" and its compactifications to ensure
the absence of global symmetries, thus providing an interesting prediction of
the Cobordism Conjecture for non-supersymmetric type IIB backgrounds.
  A major component of the present work is the explicit derivation of the
involved bordism groups as well as their generators, which correspond to
asymptotic boundaries of explicit string theory backgrounds. The main tool is
the Adams spectral sequence, to which we provide a detailed introduction. We
anticipate that the same techniques can be applied in a wide variety of
settings.
