94 citations · 371 across the 22 of their papers we have counts for
22 papers
Homological mirror symmetry of via Morse homotopy
Masahiro Futaki, Hiroshige Kajiura
This is a sequel to our paper arXiv:2008.13462, where we proposed a definition of the Morse homotopy of the moment polytope of toric manifolds. Using this as the substitute of the…
Homological mirror symmetry of and their products via Morse homotopy
Masahiro Futaki, Hiroshige Kajiura
We propose a way of understanding homological mirror symmetry when a complex manifold is a smooth compact toric manifold. So far, in many example, the derived category $D^b(coh(X))…
Fukaya categories of two-tori revisited
Hiroshige Kajiura
We construct an A-infinity structure of the Fukaya category explicitly for any flat symplectic two-torus. The structure constants of the non-transversal A-infinity products are obt…
Comments on the shifts and the signs in A-infinity categories
Hiroshige Kajiura
We discuss that there exist at least two different choices in the signs of the induced A-infinity structures in shifting the degree of objects in an A-infinity category. We show th…
Homotopy theory of -algebras and characteristic classes of fiber bundles
Hiroshige Kajiura, Takahiro Matsuyuki, Yuji Terashima
In this paper we give a Chern-Weil-type construction of characteristic classes of fiber bundles, based on homotopy theory of C-infinity algebras. Our idea is to replace a family of…
Triangulated categories of matrix factorizations for regular systems of weights with
Hiroshige Kajiura, Kyoji Saito, Atsushi Takahashi
We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of we…