Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in $\Z\oplus \Z_2$. We also show in each setting that the group of values for the index (either $\Z$ or $\Z\oplus \Z_2$) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which charaterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds.Comment: 29 page

Probing the X(4350)X(4350) in γγ\gamma \gamma interactions at the LHC

The production of $X(4350)$ in the $\gamma \gamma$ interactions that occur in proton-proton, proton-nucleus and nucleus-nucleus collisions at the CERN Large Hadron Collider (LHC) is investigated and predictions for the kinematical ranges probed by the ALICE and LHCb Collaborations are presented. We focus on the $\gamma \gamma \rightarrow \phi J/\Psi$ process, which have been measured by the Belle Collaboration, and present parameter free predictions for the total cross sections at the LHC energies. Our results demonstrate that the experimental study of this process is feasible and can be used to confirm or not the existence of the $X(4350)$ state. Finally, for completeness, we present predictions for the production of the $X(3915)$ state in the $\gamma \gamma \rightarrow \omega J/\Psi$ process and show that this exotic state can also be probed in $\gamma \gamma$ interactions at the LHC.Comment: 5 pages, 2 figures, 2 table