D-Branes on Spaces Stratified Fibered Over Hyperbolic Orbifolds

TL;DR

This paper explores the mathematical framework of K-theory and homology to analyze D-branes on spaces fibered over hyperbolic orbifolds, providing criteria for stability and insights into charge structures.

Contribution

It introduces a novel application of algebraic K-theory and spectral sequences to understand D-branes on complex stratified fibered spaces over hyperbolic orbifolds, linking physical properties with advanced mathematics.

Findings

D-branes properties are fully described within K-theory.

Criteria for D-brane stability on negatively curved groups are established.

Charge structures of branes on stratified fibered spaces are characterized.

Abstract

We apply the methods of homology and K-theory for branes wrapping spaces stratified fibered over hyperbolic orbifolds. In addition, we discuss the algebraic K-theory of any discrete co-compact Lie group in terms of appropriate homology and Atiyah-Hirzebruch type spectral sequence with its non-trivial lift to K-homology. We emphasize the fact that the physical D-branes properties are completely transparent within the mathematical framework of K-theory. We derive criteria for D-brane stability in the case of strongly virtually negatively curved groups. We show that branes wrapping spaces stratified fibered over hyperbolic orbifolds carry charge structure and change the additive structural properties in K-homology.