This is kind of a strange and vague question... sorry about that.


I am really interested in $G\_2$ Twisted Connected sums as described in this paper: <https://arxiv.org/abs/math/0012189> "Twisted connected sums and special Riemannian holonomy" by Alexei Kovalev. I would like to use those constructions to come up with examples to test new ideas.


Some people have told me that this paper is "not taken seriously" because there are mistakes in it. These people were not sufficiently familiar with the paper to tell me *what the mistakes were* and whether or not they had been corrected.


I have found maybe one or two mistakes but they are very small. More like typos.


Does anyone here know what the "mistakes" are (if there are any) or what the story is behind these rumors?



Are there mistakes in Kovalev's "Twisted connected sums and special Riemannian holonomy"?
The error in Kovalev's paper is described in [arXiv:1206.227](https://arxiv.org/abs/1206.2277) (see the discussion following theorem 2.6). An alternative proof is in [arXiv:1212.6929.](https://arxiv.org/abs/1212.6929)



> 
> Building on the previous work of Tian–Yau, Kovalev claimed to prove
> the existence of exponentially asymptotically cylindrical Calabi–Yau
> manifolds, improving substantially the asymptotics previously
> established by Tian–Yau. Unfortunately Kovalev’s proof of the improved
> asymptotics contains an error (it crucially relies on a Euclidean type
> Sobolev inequality that fails for any volume growth rate less than the
> maximal one). Other errors in Kovalev occur in the construction of
> hyper-Kähler rotations (especially Lemma 6.47 which is used in the
> proof of the main Theorem 6.44).
> 
> 
> 


