arXiv subjects

Sh. Shakirov

Publications and source records attributed to Sh. Shakirov.

38 records · Page 3Linked to original sources

arXiv2007

A-infinity structure on simplicial complexes

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as anticipated, it is a part of non-trivial A-infinity structure, involving a chain of poly-linear operations, constrained by nilpotency relation: (d + \wedge + m + ...)^n = 0 with n=2.

math.GT↗

arXiv2007

Higher Nilpotent Analogues of A-infinity Structure

Higher nilpotent analogues of the $A-\infty$-structure are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of /hep-th/0704.2609. These structures are associated with the higher nilpotent differential $d_n$, satisfying $d_n^n =0$, which is naturally defined on triangulated manifolds (tetrahedral lattices). The deformation $D_n = (I + ε_n) d_n (I + ε_n)^{-1}$ is defined with the help of the $n$-versions of discrete exterior product $\wedge_n$ and the $K_n$-operator.

hep-th↗