Hex is usually played on a parallelogram shaped board. What if you play it on a Torus?

One thing I notice is that the idea of connecting opposite sides doesn't make much sense anymore, since a torus has no sides.

What you can do is assign the players target "loops", where two loops are considered equivalent if they can continuously deformed into each other. If two loops are different, they will intersect, unless one of the loops is contractible. That means that if the two players set of "victory" loops is disjoint, one player winning stops the other player from wi

Has there been any research done on Torus-shaped-board Hex games?

Hex is usually played on a parallelogram shaped board. What if you play it on a Torus?

One thing I notice is that the idea of connecting opposite sides doesn't make much sense anymore, since a torus has no sides.

What you can do is assign the players target "loops", where two loops are considered equivalent if they can continuously deformed into each other. If two loops are different, they will intersect, unless one of the loops is contractible. That means that if the two players set of "victory" loops is disjoint, one player winning stops the other player from winning.

Has there been any research done on Torus-shaped-board Hex games?