Abstract
We compute the Moore–Witten regularized –plane integral on , and we confirm the conjecture that it is the generating function for the –Donaldson invariants of . We also derive generating functions for the –Donaldson invariants with massless monopoles using the geometry of certain rational elliptic surfaces (), and we show that the partition function for is nearly modular. Our results rely heavily on the theory of mock theta functions and harmonic Maass forms (for example, see Ono [Current developments in mathematics, 2008, Int. Press, Somerville, MA (2009) 347–454]).
Citation
Andreas Malmendier. Ken Ono. "$\mathrm{SO}(3)$–Donaldson invariants of $\mathbb{C}\mathrm{P}^2$ and mock theta functions." Geom. Topol. 16 (3) 1767 - 1833, 2012. https://doi.org/10.2140/gt.2012.16.1767
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