Erratum to appendix to “Algebraic torsion in contact manifolds” by Latschev and Wendl

I made an embarassing error in the appendix that I wrote to the paper “Algebraic torsion in contact manifolds” by Janko Latschev and Chris Wendl.  Fortunately the error is easy to fix.

The error is that in Definition A.4, I gave two definitions of and claimed that they were equivalent.  However they are not equivalent.  The first definition can be bigger than the second definition.

I actually just wanted the second definition, so to fix this, simply the delete the first definition. Definitions A.5 and A.8 also need to be modifed analogously.  Finally, the words “and only if” need to be removed from the sentence immediately following Definition A.4.  The rest of the appendix then works fine.

Thanks to Cagatay Kutluhan for pointing this out (several months ago), and sorry for taking so long to post this and for being so careless.  It’s all the more unforgivable because when writing this I had the feeling that I really should check the spectral sequence stuff more carefully (because it is so easy to make mistakes with this) and then was too lazy to do so.