The Universal Coefficient Theorem, Wormholes, and the Island

Abstract: I analyse the extension of the Ryu Takayanagi formula from the perspective of the universal coefficient theorem and cohomology with different coefficients. Looking at the axioms of cohomology, the so called Eilenberg-Steenrod axioms, the third axiom states that the cohomology of a point is trivial in all orders. If this axiom is abandoned the point may have additional structure. This phenomenon is not unusual in physics, a simple example for that being the spin structure or even the point particle to string transition. I studied the transition between different coefficients in cohomology and hence between different structures of the geometrical point by means of the universal coefficient theorem. The results may have impact on recent island calculations of the black hole radiation entropy and the Page curve as well as on a potential mapping of higher genus diagrams to genus one diagrams in the topological expansion of string theory.