Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Tudor Pădurariu, Yukinobu Toda, , ,
| Summary:
In previous works, we introduced and studied certain categories called
quasi-BPS categories associated to symmetric quivers with potential,
preprojective algebras, and local surfaces. They have properties reminiscent of
BPS invariants/ cohomologies in enumerative geometry, for example they play
important roles in categorical wall-crossing formulas.
In this paper, we make the connections between quasi-BPS categories and BPS
cohomologies more precise via the cycle map for topological K-theory. We show
the existence of filtrations on topological K-theory of quasi-BPS categories
whose associated graded are isomorphic to the monodromy invariant BPS
cohomologies. Along the way, we also compute the topological K-theory of
categories of matrix factorizations in terms of the monodromy invariant
vanishing cycles (a version of this comparison was already known by work of
Blanc-Robalo-To"en-Vezzosi), prove a Grothendieck-Riemann-Roch theorem for
matrix factorizations, and prove the compatibility between the Koszul
equivalence in K-theory and dimensional reduction in cohomology.
In a separate paper, we use the results from this paper to show that the
quasi-BPS categories of K3 surfaces recover the BPS invariants of the
corresponding local surface, which are Euler characteristics of Hilbert schemes
of points on K3 surfaces.
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