3,705 research outputs found
A survey on the local divisor technique
© 2015 Elsevier B.V. Local divisors allow a powerful induction scheme on the size of a monoid. We survey this technique by giving several examples of this proof method. These applications include linear temporal logic, rational expressions with Kleene stars restricted to prefix codes with bounded synchronization delay, Church-Rosser congruential languages, and Simon's Factorization Forest Theorem. We also introduce the notion of a localizable language class as a new abstract concept which unifies some of the proofs for the results above
Construction of G_2-instantons via twisted connected sums
We propose a method to construct G_2-instantons over a compact twisted
connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski
to instantons over a pair of 7-manifolds with a tubular end (see
arXiv:1310.7933). In our example, the moduli spaces of the ingredient
instantons are non-trivial, and their images in the moduli space over the
asymptotic cross-section K3 surface intersect transversely. Such a pair of
asymptotically stable holomorphic bundles is obtained using a twisted version
of the Hartshorne-Serre construction, which can be adapted to produce other
examples. Moreover, their deformation theory and asymptotic behaviour are
explicitly understood, results which may be of independent interest.Comment: 22 pages. Final version to appear in Mathematical Research Letter
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