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In the following work, an attempt to conciliate the Ricci flow conjecture andthe Cobordism conjecture, stated as refinements of the Swampland distanceconjecture and of the No global symmetries conjecture respectively, ispresented. This is done by starting from a suitable manifold with trivialcobordism class, applying surgery techniques to Ricci flow singularities andtrivialising the cobordism class of one of the resulting connected componentsvia the introduction of appropriate defects. The specific example of$\Omega^{SO}_4$ is studied in detail. A connection between the process ofblowing up a point of a manifold and that of taking the connected sum of suchwith $\mathbb{CP}^n$ is explored. Hence, the problem of studying the Ricci flowof a $K3$ whose cobordism class is trivialised by the addition of $16$ copiesof $\mathbb{CP}^2$ is tackled by applying both the techniques developed in theprevious sections and the classification of singularities in terms of ADEgroups.

Cobordism, Singularities and the Ricci Flow Conjecture