Nilpotency in instanton homology, and the framed instanton homology of a surface times a circle

Abstract

In the description of the instanton Floer homology of a surface times a circle due to Muñoz, we compute the nilpotency degree of the endomorphism $u^2-64$. We then compute the framed instanton homology of a surface times a circle with non-trivial bundle, which is closely related to the kernel of $u^2-64$. We discuss these results in the context of the moduli space of stable rank two holomorphic bundles with fixed odd determinant over a Riemann surface.

28 pages, comments welcome

References in corpus (1)

• Instantons and odd Khovanov homology

Cited by in corpus (3)

• Framed instanton homology and concordance
• Instanton Floer homology of almost-rational plumbings
• The cohomology of rank two stable bundle moduli: mod two nilpotency & skew Schur polynomials