Title: Möbius topological superconductivity in UPt$_3$,
Abstract: Intensive studies for more than three decades have elucidated multiple
superconducting phases and odd-parity Cooper pairs in a heavy fermion
superconductor UPt$_3$. We identify a time-reversal invariant superconducting
phase of UPt$_3$ as a recently proposed topological nonsymmorphic
superconductivity. Combining the band structure of UPt$_3$, order parameter of
$E_{\rm 2u}$ representation allowed by $P6_3/mmc$ space group symmetry, and
topological classification by $K$-theory, we demonstrate the nontrivial
$Z_2$-invariant of three-dimensional DIII class enriched by glide symmetry.
Correspondingly, double Majorana cone surface states appear at the surface
Brillouin zone boundary. Furthermore, we show a variety of surface states and
clarify the topological protection by crystal symmetry. Majorana arcs
corresponding to tunable Weyl points appear in the time-reversal symmetry
broken B-phase. Majorana cone protected by mirror Chern number and Majorana
flat band by glide-winding number are also revealed.