Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Families of $A_\infty$ algebras and homotopy group actions   We define homotopy group actions in terms of families of $A_\infty$ algebras
indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism
induced by a path on the manifold and for the $A_\infty$ homotopy corresponding
to a pair of homotopic paths. Finally, we compute examples for finite groups
and finitely generated free nonabelian groups and determine that every homotopy
group action by a finite group is homotopic to a strict group action.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys