A bstract Non-trivial K-theory groups and non-trivial cobordism can lead to global symmetries which are conjectured be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, considered as physical manifestation of generalisation classic Conner-Floyd isomorphism. The picture is exemplified relations KO-groups Spin-cobordisms K-group...

We study left-hand side restrictions of the induced subgraph isomorphism problem: Fixing a class C, for given graphs G ∈ C and arbitrary H we ask for induced subgraphs of H isomorphic to G. For the homomorphism problem this kind of restriction has been studied by Grohe and Dalmau, Kolaitis and Vardi for the decision problem and by Dalmau and Jonsson for its counting variant. We give a dichotomy...

Let M be a connected compact orientable surface and let P either the real line ℝ or circle S1. The group D(M) of diffeomorphisms on acts in space smooth mappings C∞(M,P) by rule (f, h) ⟼ f ° h, where h ∈ C∞(M,P). For C∞(M,P), O(f) denote orbit relative to specified action. By ℳ(M,P) we set isomorphism classes for fundamental groups