Topology of Black Holes' Horizons

The Möbius strip spacetime topology and the entangled antipodal points on black hole surfaces, recently described by ‘t Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem from algebraic topology.  Considering this observation and other recent claims which suggest that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel topological framework can be developed: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles.  This allows us to achieve a mathematical description of the holographic principle occurring in S².  Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.