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one and talk about connected sum connected sum the connected sum of two topological spaces x and y is given by this x y and this is obtained by removing a small disk disk from each other in fact instead of a small disk you can also think of it as a small triangle as well because a disc and a triangle theyre homomorphic to each other and this if this disc is solid the triangle also has to be solid otherwise it wont work so let me write triangle as well triangle from each other and connecting the resulting holes connecting the resulting holes with the cylinder so this is how it would look like lets say this is a torus we want to have the connected sum of this with another torus then what i can do i can remove a small disc from here remove a small disk from here and connect them with a cylinder right so if i do that the resulting figure would look something like this this is one torus this is a another torus and this is our cylinder that connects them okay and this idea actually helps
