Union of locally flat cells.

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2 total messages Started by le Fri, 28 Aug 1992 10:47

#44

Author: le
Date: Fri, 28 Aug 1992 10:47

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1. Can anyone give information about the current status
of the "annulus conjecture" ?
Rushing stated in his book "Topological Embeddings, AP 1973"
that "it is still unknown for n=4".

2. Is the \beta-statement \beta(n,n-1,n-1,n-2) true for n=3 ?
If not, under what additional conditions it it true ?
Rushing states in his book that it is true for n > 3.

Any suggestions, hints are welcome.

Thanks in advance.

Re: Union of locally flat cells.

#45

Author: john klein
Date: Fri, 28 Aug 1992 14:01

21 lines
1460 bytes

In article <BtowMx.M9p@fuhainf.fernuni-hagen.de> le@tinosfernuni-hagen.de  
writes:
> 
> 1. Can anyone give information about the current status
> of the "annulus conjecture" ?
> Rushing stated in his book "Topological Embeddings, AP 1973"
> that "it is still unknown for n=4".
> 
> 2. Is the \beta-statement \beta(n,n-1,n-1,n-2) true for n=3 ?
> If not, under what additional conditions it it true ?
> Rushing states in his book that it is true for n > 3.
> 
> Any suggestions, hints are welcome.
> 
> Thanks in advance.

I believe that Quinn proved the 4-dimensional annulus conjecture.
The paper was published in the Journal of Differential Geometry
(1984?). The precise reference is in the Freedman-Quinn  book
"Topology of 4-manifolds" (Princeton , 1991)
Andrew Ranicki

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