arXiv subjects

Khaled Qazaqzeh

Publications and source records attributed to Khaled Qazaqzeh.

21 records · Page 2Linked to original sources

arXiv2005

Integral Bases for Certain TQFT-Modules of the Torus

We find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus over given rings of integers. We use variant of the bases defined in [GMW]for the lattices of the SO(3)-TQFT-theory modules of the torus. Moreover, we discuss the quantization functors (V_{p},Z_{p}) for p=1, and p=2. Then we give concrete bases for the lattices of the modules in the 2-theory. We use the above results to discuss the ideal invariant defined in [FK]. The ideal can be computed for all 3-manifolds using the 2-theory, and all 3-manifolds with torus boundary using the SU(2)-TQFT-theory. In fact, we show that this ideal in the SU(2)-TQFT-theory is contained in the product of the ideals in the 2-theory and the SO(3)-TQFT-theory under a certain change of cofficients, and it is equal in the case of a torus boundary.

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arXiv2005

Periodic 3-Manifolds and Modular Categories

A p-periodic 3-manifold is a 3-manifold that admits a Z_{p}-action whose fixed point set is a circle. We give a congruence relates the quantum invariant of a p-periodic 3-manifold associated to any modular category over an integrally closed ground ring and the corresponding quantum invariant of its orbit space.

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arXiv2005

The parity of the Maslov index and the even cobordism category

We give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over the real numbers. We define an index two subcategory (the even subcategory) of a 3-dimensional cobordism category. The objects of the category are surfaces are equipped with Lagrangian subspaces of their real first homology. This generalizes a result of the first author where surfaces are equipped with Lagrangian subspaces of their rational first homology.

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