Topological K-theory of quasi-BPS categories of symmetric quivers with potential
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918409878372352 |
|---|---|
| author | Pădurariu, Tudor Toda, Yukinobu |
| author_facet | Pădurariu, Tudor Toda, Yukinobu |
| contents | 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-Toën-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08432 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological K-theory of quasi-BPS categories of symmetric quivers with potential Pădurariu, Tudor Toda, Yukinobu Algebraic Geometry Representation Theory 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-Toën-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. |
| title | Topological K-theory of quasi-BPS categories of symmetric quivers with potential |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2309.08432 |