Calabi-Yau structures on topological Fukaya categories

We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the topological dualizing sheaf - specializes to the classical notion of orientation when applied to the category of local systems on a manifold. We apply this construction to the cosheaves on arboreal skeleta arising in the microlocal approach to the A-model.Comment: 88 pages, 15 figure

A support theorem for Hilbert schemes of planar curves

Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve encodes the cohomology of all Hilbert schemes of points on the curve. Globally, it follows that a family of such curves with smooth relative compactified Jacobian ("moduli space of D-branes") in an irreducible curve class on a Calabi-Yau threefold will contribute equally to the BPS invariants in the formulation of Pandharipande and Thomas, and in the formulation of Hosono, Saito, and Takahashi.Comment: 13 pages. (v2 updated to match published version.

Half-Duplex or Full-Duplex Relaying: A Capacity Analysis under Self-Interference

In this paper multi-antenna half-duplex and full-duplex relaying are compared from the perspective of achievable rates. Full-duplexing operation requires additional resources at the relay such as antennas and RF chains for self-interference cancellation. Using a practical model for the residual self-interference, full-duplex achievable rates and degrees of freedom are computed for the cases for which the relay has the same number of antennas or the same number of RF chains as in the half-duplex case, and compared with their half-duplex counterparts. It is shown that power scaling at the relay is necessary to maximize the the degrees of freedom in the full-duplex mode.Comment: New references added and some typos have been corrected. 6 Pages, 5 Figures. Accepted for publication in the CISS-201