[Grammar] without his teacher knowing

[Oceanlike]

Is it correct to use "knowing" in (a)?
(a) He signed up for the competition without his teacher knowing.

Does (b) have the same meaning as (a)?
(b) He signed up for the competition without his teacher's knowledge.

If (a) and (b) are correct but different, what is the difference?

 

[Rover_KE]

(a) Yes.

(b) Yes.

(c) They mean the same to me.

 

[Tdol]

Theoretically, b) could mean that he was ignorant of what his teacher knew, but that is not an obvious interpretation.