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arXiv · 1502.07560

Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds

Andrey A. Bytsenko·Richard J. Szabo·Anca Tureanu
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Abstract

We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and K-homology. We propose a definition of Type II string theory on such backgrounds that further carry stratified systems of fiber bundles, which generalise the more conventional orbifold and symmetric string backgrounds, together with a classification of wrapped branes by a suitable generalized homology theory. For spaces stratified fibered over hyperbolic orbifolds we use the algebraic K-theory of their fundamental groups and Quinn homology to derive criteria for brane stability in terms of an Atiyah-Hirzebruch type spectral sequence with its lift to K-homology. Stable D-branes in this setting carry stratified charges which induce new additive structures on the corresponding K-homology groups. We extend these considerations to backgrounds which support H-flux, where we use K-groups of twisted group algebras of the fundamental groups to analyse stability of locally symmetric spaces with K-amenable isometry groups, and derive stability conditions for branes wrapping the fibers of an Eilenberg-MacLane spectrum functor.

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Andrey A. Bytsenko, Richard J. Szabo, Anca Tureanu. 2015-02-26. Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds. https://doi.org/10.1088/1751-8113/49/16/165401

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