Contribution to the Odonata of the Kingdom of Tonga

New data on the Odonata fauna of the Kingdom of Tonga is provided following re-search carried out on Tongatapu and 'Eua islands in July 2012. New localities for Tongatapu Island are put on record and previous studies are compared with new pheno-logical data from a period during which field surveys are rarely conducted on Pacific islands. Although Odonata have been collected before from 'Eua Island, the data presented here is the first published so far. 'Eua Island is assessed as a very important venue for further research on Odonata. Overall the Kingdom of Tonga is very depauperate in water resources with lotic biotopes very restricted in area and found on 'Eua Island, and possibly on Tofua and Late islands, which are both volcanic. This study on the Odonata of 'Eua resulted in records of eighttaxa, including with Teinobasis sp. nov., which will be described elsewhere. Morphological variation in Pseudagrion microcephalum stainbergerorumand Trameatransmarinaare discussed in the context of their subspecific affiliation. Diagnostic features for easier differentiation are proposed for the first of these taxa; the validation of commonly used diagnostic traits is discussed for the second

Recovering the topology of surfaces from cluster algebras

We present an effective method for recovering the topology of a bordered oriented surface with marked points from its cluster algebra. The information is extracted from the maximal triangulations of the surface, those that have exchange quivers with maximal number of arrows in the mutation class. The method gives new proofs of the automorphism and isomorphism problems for the surface cluster algebras, as well as the uniqueness of the Fomin-Shapiro-Thurston block decompositions of the exchange quivers of the surface cluster algebras. The previous proofs of these results followed a different approach based on Gu's direct proof of the last result. The method also explains the exceptions to these results due to pathological problems with the maximal triangulations of several surfaces.Comment: 29 pages, AMS Late