A vanishing result for a Casson-type instanton invariant
arXiv:0911.2772 · doi:10.1112/plms/pdu030
Abstract
Casson-type invariants emerging from Donaldson theory over certain negative definite 4-manifolds were recently suggested by Andrei Teleman. These are defined by a count of a zero-dimensional moduli space of flat instantons. Motivated by the cobordism program of proving Witten's conjecture, we use a moduli space of PU(2) Seiberg-Witten monopoles to exhibit an oriented one-dimensional cobordism of the instanton moduli space to the empty space. The Casson-type invariant must therefore vanish.
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- Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant