arXiv subjects

Irving Dai

Publications and source records attributed to Irving Dai.

22 records · Page 2Linked to original sources

arXiv2017

Involutive Heegaard Floer homology and plumbed three-manifolds

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.

math.GT↗

arXiv2017

On the Pin(2)-equivariant monopole Floer homology of plumbed 3-manifolds

We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Ozsvath and Szabo). We show that for these manifolds, the Pin(2)-equivariant monopole Floer homology can be calculated in terms of the Heegaard Floer/monopole Floer lattice complex defined by Nemethi. Moreover, we prove that in such cases the ranks of the usual monopole Floer homology groups suffice to determine both the Manolescu correction terms and the Pin(2)-homology as an abelian group. As an application of this, we show that $β(-Y, s) = \barμ(Y, s)$ for all plumbed 3-manifolds with at most one bad vertex, proving a conjecture posed by Manolescu. Our proof also generalizes results by Stipsicz and Ue relating the Neumann-Siebenmann invariant with the Ozsvath-Szabo $d$-invariant.

math.GT↗

arXiv2013

Properties of Full-Flag Johnson Graphs

We introduce and study a variant of the family of Johnson graphs, the Full-Flag Johnson graphs. We show that Full-Flag Johnson graphs are Cayley graphs on S_n generated by certain classes of permutations, and that they are in fact generalizations of permutahedra. We derive some results about the adjacency matrices of Full-Flag Johnson graphs and apply these to the set of permutahedra to deduce part of their spectra.

math.CO↗

arXiv2013

On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations

We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and consider their relation to other notions of mixing in infinite measure.

math.DS↗