  We analyze a particle constrained to move on a $(p,q)$-torus knot within the
framework of supervariable approach and deduce the BRST as well as anti-BRST
symmetries. We also capture the nilpotency and absolute anti-commutativity of
(anti-)BRST symmetries in this framework. Further, we show the existence of
some novel symmetries in the system such as (anti-)co-BRST, bosonic, and ghost
scale symmetries. We demonstrate that the conserved charges (corresponding to
these symmetries) adhere to an algebra which is analogous to that of de Rham
cohomological operators of differential geometry. As the charges (and the
symmetries) find a physical realization with the differential geometrical
operators, at the algebraic level, the present model presents a prototype for
Hodge theory.
