Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to discretize the differential forms on the interval   We provide explicit quasi-isomorphisms between the following three algebraic
structures associated to the unit interval: i) the commutative dg algebra of
differential forms, ii) the non-commutative dg algebra of simplicial cochains
and iii) the Whitney forms, equipped with a homotopy commutative and homotopy
associative, i.e. $C_\infty$, algebra structure. Our main interest lies in a
natural `discretization' $C_\infty$ quasi-isomorphism $\varphi$ from
differential forms to Whitney forms. We establish a uniqueness result that
implies that $\varphi$ coincides with the morphism from homotopy transfer, and
obtain several explicit formulas for $\varphi$, all of which are related to the
Magnus expansion. In particular, we recover combinatorial formulas for the
Magnus expansion due to Mielnik and Pleba\'nski.

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin