Hi Dr. Moskovich.

I think Manolescu is implicitly implied after the statement “ and are both nonzero” (page 7, 1st paragraph) to draw the conclusion that is not simplicially triangulable.

Can anyone tell me if I’m correct/incorrect here?

The claim that the “Galewski-Stern 5-manifold” is not triangulable is where they are using Manolescu.

Bravo! The plot thickens! There are aspherical non-triangulable manifolds in dimension .

]]>Hi Professor Putnam,

I guess I missed that. Where in their paper do they assume Manolescu’s theorem in their proof?

It is not accurate to say that Davis-Fowler-Lafont use different techniques than Manolescu. In fact, they do not give an independent proof of Manolescu’s theorem; rather, they assume it and then show that using it together with some other techniques one can produce non-triangulatable manifolds which are also aspherical.

]]>Hi Dr. Moskovich,

as Professor Stern pointed out in comment 3 below, you can have non-simplicially triangulable ORIENTABLE compact manifolds in dimension greater than or equal to 6.

[silly comment of mine deleted]

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