# The definition of tori – topology

The question may seem silly, but I do not find the answer.

For me, the $$n-$$torus is “an sphere with $$n$$ holes”.

Topologically, this is called the connected sum of $$n$$ tori, is it right?

What about the $$T^n=overbrace{S^1times cdots times S^1}^{n ,times}$$, what is its name and what are its properties?

Do the two surfaces have some relation?

Thank you so much.