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Register a new userInvolutive Heegaard Floer homology and plumbed three-manifolds
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We compute the involutive Heegaard Floer homology of the family of three-manifolds obtained by plumbings along almost-rational graphs. (This includes all Seifert fibered homology spheres.) We also study the involutive Heegaard Floer homology of connected sums of such three-manifolds, and explicitly determine the involutive correction terms in the case that all of the summands have the same orientation. Using these calculations, we give a new proof of the existence of an infinite-rank subgroup in the three-dimensional homology cobordism group.
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In cite{MR1957829}, Ozsvath and Szabo use Heegaard Floer homology to define numerical invariants $d_{1/2}$ and $d_{-1/2}$ for 3-manifolds $Y$ with $H_{1}(Y;mathbb{Z})cong mathbb{Z}$. We define involutive Heegaard Floer theoret
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