In this article, we continue our study of 'Frobenius structures' and
symplectic spectral invariants in the context of symplectic spinors. By
studying the case of C1-small Hamiltonian mappings on symplectic manifolds
M admitting a metaplectic structure and a parallel O^(n)-reduction of
its metaplectic frame bundle we derive how the construction of 'singularly
rigid' resp. 'self-dual' pairs of irreducible Frobenius structures associated
to this Hamiltonian mapping Ξ¦ leads to a Hopf-algebra-type structure on
the set of irreducible Frobenius structures. We then generalize this
construction and define abstractly conditions under which 'dual pairs'
associated to a given C1-small Hamiltonian mapping emerge, these dual pairs
are esssentially pairs (s1β,J1β),(s2β,J2β) of closed sections of the
cotangent bundle TβM and (in general singular) comptaible almost complex
structures on M satisfying certain integrability conditions involving a
Koszul bracket. In the second part of this paper, we translate these
characterizing conditions for general 'dual pairs' of Frobenius structures
associated to a C1-small Hamiltonian system into the notion of matrix
factorization. We propose an algebraic setting involving modules over certain
fractional ideals of function rings on M so that the set of 'dual pairs' in
the above sense and the set of matrix factorizations associated to these
modules stand in bijective relation. We prove, in the real-analytic case, a
Riemann Roch-type theorem relating a certain Euler characteristic arising from
a given matrix factorization in the above sense to (integral) cohomological
data on M using Cheeger-Simons-type differential characters, derived from a
given pair (s1β,J1β),(s2β,J2β). We propose extensions of these techniques
to the case of 'geodesic convexity-smallness' of Ξ¦ and to the case of
general Hamiltonian systems on M.Comment: 24 pages, minor corrections in statement and proof of Theorem 1.11,
this paper builds in content, notation and referencing on arXiv:1411.423