Let X be a complex K3 surface, $$\textrm{Diff}(X)$$ the group of diffeomorphisms and $$\textrm{Diff}_0(X)$$ identity component. We prove that fundamental contains free abelian countably infinite rank as direct summand. The summand is detected using families Seiberg–Witten invariants. moduli space Einstein metrics on used key ingredient in proof.

A family of k-element subsets an n-element set is called 3-wise intersecting if any three members in the have non-empty intersection. We determine maximum size such families exactly or asymptotically. One our results shows that for every ?>0 there exists n0 n>n0 and 25+?<kn<12?? then 4(n?4k?3)+(n?4k?4).

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

We consider black holes in EYM theory with a negative cosmological constant. The solutions obtained are somewhat different from those for which the cosmological constant is either positive or zero. Firstly, regular black hole solutions exist for continuous intervals of the parameter space, rather than discrete points. Secondly, there are non-trivial solutions in which the gauge field has no nod...