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2. Rank-reduction wall-crossing


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      Problem 2.1.

      Let $S$ be a surface of general type. Express rank $r$ Vafa-Witten invariants on $S$ in terms of rank 1 Vafa-Witten invariants of $S$ via wall-crossing.


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          Problem 2.2.

          Let $S$ be a surface of general type. Use wall-crossing to find an explicit (possibly conjectural) formula for rank $r=4$ Vafa-Witten invariants of $S$.


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              Problem 2.3.

              Extend the rank reduction techniques of Feyzbakhsh-Thomas to include refined invariants (e.g. motivic invariants).

                  Cite this as: AimPL: Wall-crossing: techniques and applications, available at http://aimpl.org/wallcrossing.