Is there any specific name for a coffee cup handle in mathematics?

[princy]

is there any specific name for a coffee cup handle in mathematics?

 

[sutupidmath]

Torus

 

[mathwonk]

maybe a solid torus? a torus is technically a surface formed as a cross product of two circles.

 

[princy]

Torus

i think torus is wrong.. is there any name for a bend like structure?

 

[HallsofIvy]

? What do you mean by a "bend like structure". A coffee cup handle and, indeed, the entire coffee cup is topologically equivalent to a "solid" torus.

 

[Petek]

This is way out of my comfort zone, but aren't the structures described by the OP sometimes called handles? Such as here.

 

[mathwonk]

are we going in circles? that's what the OP said.

 

[HallsofIvy]

Yep! Sometimes we call a handle a handle!

 

[redbowlover]

i'm curious about the context of the question. a solid handle by itself is contractible and so mathematicians wouldn't bother giving it a name. but we often refer to "handles" when we are attaching them to other spaces. a coffee cup handle would be a 3-handle...if you attached a 3-handle to a solid ball you get a torus. in this context it makes sense to name the "handle". but i would say in general, the coffee cup handle is trivial. anyone agree?

 

[HallsofIvy]

Well, if it is not attached to something, in what sense is it a "handle"?

 

[homology]

i'm curious about the context of the question. a solid handle by itself is contractible and so mathematicians wouldn't bother giving it a name. but we often refer to "handles" when we are attaching them to other spaces. a coffee cup handle would be a 3-handle...if you attached a 3-handle to a solid ball you get a torus. in this context it makes sense to name the "handle". but i would say in general, the coffee cup handle is trivial. anyone agree?

as mentioned above, technically the torus is 'hollow' the 'filled in' torus you describe is different topologically than S^1\times S^1 in that its fundamental group is just Z instead of ZxZ.