The one of numerical Campedelli surfaces cannot be the symmetry group of order 3.
The one of numerical Campedelli surfaces cannot be the symmetry group of order 3. This property of knot complements is (**) obtained from the over presentation of a knot by applying the Tietze operations. The one of the Poincare homology sphere is isomorphic to the binary icosahedral group, which is the only finite one for 3-manifolds except for (*) the one for the 3-sphere. The one of the Klein bottle is isomorphic to the direct sum of a copy of the integers and the integers modulo 2, while the one of a torus of genus g is isomorphic to g copies of the integers. For a sphere of dimension greater than or equal to two, it is isomorphic to a point, and for a circle it is isomorphic to the integers. FTP, name this group formed by the set of equivalence classes of all loops, the simplest homotopy group.
The one of numerical Campedelli surfaces cannot be the symmetry group of order 3.
fundamental group 