Takuro Mochizuki

The 3-cocycles of the Alexander quandles F q (T )/(T −!)

We determine the third cohomology of Alexander quandles of the form F_q[T]/(T-omega), where F_q denotes the finite field of order q and omega is an element of F-q which is neither 0 nor 1. As a result, we obtain many concrete examples of non-trivial 3-cocycles.

Harmonic Bundles and Toda Lattices With Opposite Sign II

We study the integrable variation of twistor structure associated to any solution of the Toda lattice with opposite sign. In particular, we give a criterion when it has an integral structure. It follows from two results. One is the explicit computation of the Stokes factors of a certain type of meromorphic flat bundles. The other is an explicit description of the meromorphic flat bundle associated to the solution of the Toda equation. We use the opposite filtration of the limit mixed twistor structure with an induced torus action.

A twistor approach to the Kontsevich complexes

We study the V-filtration of the mixed twistor

Good Mixed Twistor \(\mathcal{D}\)-Modules

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Mixed Twistor \mathcal{D}-Modules

D-modules associated to algebraic meromorphic functions. We prove that their relative de Rham complexes are quasi-isomorphic to the family of Kontsevich complexes. It reveals a generalized Hodge theoretic meaning of Kontsevich complexes. On the basis of the quasi-isomorphism, we revisit the results on the Kontsevich complexes due to H. Esnault, M. Kontsevich, C. Sabbah, M. Saito and J.-D. Yu from a viewpoint of mixed twistor

Duality and Real Structure of Mixed Twistor \mathcal{D}-Modules

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