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A vanishing result for a Casson-type instanton invariant (2014)

Zentner, R.

Oxford University Press

In: Proceedings of the London Mathematical Society

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Publication Date: 2014-12-17

Description: Casson-type invariants emerging from Donaldson theory over certain negative-definite four-manifolds were recently suggested by Teleman. These are defined by an algebraic count of points in a zero-dimensional moduli space of flat instantons. Motivated by the cobordism programme of proving Witten's conjecture, we use a moduli space of ${\rm PU}(2)$ 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.

Print ISSN: 0024-6115

Electronic ISSN: 1460-244X

Topics: Mathematics

Published by Oxford University Press

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