52,277 research outputs found
On the Kauffman bracket skein module of the quaternionic manifold
We use recoupling theory to study the Kauffman bracket skein module of the
quaternionic manifold over Z[A,A^{-1}] localized by inverting all the
cyclotomic polynomials. We prove that the skein module is spanned by five
elements. Using the quantum invariants of these skein elements and the Z_2
homology of the manifold, we determine that they are linearly independent.Comment: corrected summation signs in figures 14, 15, 17. Other minor change
Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
We propose that symmetry protected topological (SPT) phases with crystalline
symmetry are formulated by equivariant generalized homologies over a
real space manifold with a crystalline symmetry group. The
Atiyah-Hirzebruch spectral sequence unifies various notions in crystalline SPT
phases such as the layer construction, higher-order SPT phases and
Lieb-Schultz-Mattis type theorems. Our formulation is applicable to interacting
systems with onsite and crystalline symmetries as well as free fermions.Comment: are wellcome. 64 pages, many figures and table
- …