Invariants of 3-manifolds and Dedekind sums

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The head investigator have studied the relationship between generalized Dedekind sums and modular forms. These are closely related to topological invariants of manifolds. In his paper titled "Modular forms, generalized Dedekind symbols and period polynomials", the investigator clarified the relationship between these three objects.He also applied the theory to the typical modular form -- the Eisenstein series. In his paper "Generalized Dedekind symbols associated with the Elsenstein series", he proved that Dedekind symbol associated with Bisenstein series is Apostol' s sums in essence. The paper will be published soon.He published the paper tided "The space of period polynomials" which shows that period polynomials are expressed in terms of Bernoulli polynomials. This seems very interesting.Recently he is trying to define Dedekind symbols to broader class of forms and made two preprint : "Dedekind symbols associated with Jacobi forms and their reciprocity law" and "twisted generalized Dedekind symbols"