Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912603694956544 |
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| author | Su, Tao |
| author_facet | Su, Tao |
| contents | The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson states that, a smooth Betti moduli space of complex dimension $d$ over a punctured Riemann surface has the dual boundary complex homotopy equivalent to a sphere of dimension $d-1$. Via a microlocal geometric perspective, we verify this conjecture for a class of rank $n$ wild character varieties over the two-sphere with one puncture, associated with any Stokes Legendrian link defined by an $n$-strand positive braid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01645 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity Su, Tao Algebraic Geometry Algebraic Topology Symplectic Geometry 14F45 (Primary) 53D42 (Secondary) The weak geometric P=W conjecture of L. Katzarkov, A. Noll, P. Pandit, and C. Simpson states that, a smooth Betti moduli space of complex dimension $d$ over a punctured Riemann surface has the dual boundary complex homotopy equivalent to a sphere of dimension $d-1$. Via a microlocal geometric perspective, we verify this conjecture for a class of rank $n$ wild character varieties over the two-sphere with one puncture, associated with any Stokes Legendrian link defined by an $n$-strand positive braid. |
| title | Dual boundary complexes of Betti moduli spaces over the two-sphere with one irregular singularity |
| topic | Algebraic Geometry Algebraic Topology Symplectic Geometry 14F45 (Primary) 53D42 (Secondary) |
| url | https://arxiv.org/abs/2109.01645 |