We determine the second homology group of the homological Goldman Lie algebra for an oriented surface.

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Cyclic polyphenylene sulfide (PPS) is an unavoidable byproduct of the preparation of linear PPS, one of the most important engineering plastics. Turning the waste into treasure is the best way to address byproducts, prevent pollution, and save energy and resources. Cyclic PPS’s potential to be used in supramolecular chemistry was proven as an additive to enhance the mechanical properties of polystyrene (PS)-based materials. After the addition of cyclic PPS, the toughness of poly­(styrene-co-ethyl acrylate) (PS-PEA) was approximately 4 times that of PS, and the value of Young’s modulus saw a slight increase. Cyclic PPS was found to form reversible and movable cross-links with PS-PEA and increase the homogeneity of PS-PEA. Thus, the results of this study provide not only a way to make use of cyclic PPS but also an easy and practical method to prepare reinforced PS-based polymers.

We determine the minimal number of generators of the homological Goldman Lie algebra of a surface consisting of elements of the first homology group of the surface.