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## Main Question or Discussion Point

Determine the homeomorphism classes of compact 3-manifolds obtained from D^3 by identifying finitely many pairs of disjoint disks in the boundary?

I just started reading some low dimensional topology on my own and I came across this question. I have realized that based on how the identification is done gives us various manifolds for instance if two disks are identified with identity map would give handlebody with unknotted handle. However I am having trouble determining the homeomorphism classes.

Any help would be appreciated.

Thanks

I just started reading some low dimensional topology on my own and I came across this question. I have realized that based on how the identification is done gives us various manifolds for instance if two disks are identified with identity map would give handlebody with unknotted handle. However I am having trouble determining the homeomorphism classes.

Any help would be appreciated.

Thanks