[kanonsviel]

Is this a Michael reaction?
If that's true, how could the C2 of the hexane ring become a donor?
Does that involve an E2 dehydration upon the ring?

[Grundalizer]

Yeah I'd say the picture is a little bit of a throw off.  that entire chain off the phenyl group (or cyclohexane I can't see the picture while I write this) is free to rotate.  As with temp dependant reactions, it could rotate around so the methyl group is almost near the ring, almost in it's final product position.

I'd agree and say that protonation of the alcohol (or at least leaving of the alcohol) as water is a key step, and that the double bond in the functional group chain reacts with the carbon bonded Alpha to the carbonyl and attached to the hydroxyl group.  I wish there were an easy program to draw out mechanisms with...words don't do them justice

[discodermolide]

Is this a Michael reaction?
If that's true, how could the C2 of the hexane ring become a donor?
Does that involve an E2 dehydration upon the ring?

How about this explanation:
Protonation of the OH followed by loss of water to give a C=C in the ring, then protonation of the carbonyl oxygen followed by 1,4-attack of the RING double bond to the end of the chain double bond to form the cyclic compound, which contains an enol and a positive charge at the ring junction. Re-kformation of the ketone and attack of water at the ring cation followed by re-elimination of water to give the structure.
I hope you can follow this as I have no means of submitting a scheme.

[jake.n]

Is this a Michael reaction?
If that's true, how could the C2 of the hexane ring become a donor?
Does that involve an E2 dehydration upon the ring?

How about this explanation:
Protonation of the OH followed by loss of water to give a C=C in the ring, then protonation of the carbonyl oxygen followed by 1,4-attack of the RING double bond to the end of the chain double bond to form the cyclic compound, which contains an enol and a positive charge at the ring junction. Re-kformation of the ketone and attack of water at the ring cation followed by re-elimination of water to give the structure.
I hope you can follow this as I have no means of submitting a scheme.

I agree, but you should not need to hydrate/dehydrate to reform the alkene.  You should be able to get there from the tertiary carbocation via E1.  Either way, same result.

[macman104]

E1 dehydration to form conjugated alkene followed by nazarov cyclization

[kanonsviel]

Oh, yes, that's definitely the answer.
Though I once considered the possibility of a pericyclic reaction, yet the carbonyl group is something I have never met with in this type of reactions
Thanks for your helps very much