Fibered faces, veering triangulations, and the arc complex
We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol’s veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all fibers in a given fibered face of the Thurston norm.
OBJECTIVE ::: To establish a new method to discriminate Aaron's beard by Fourier transformation infrared spectrometry. ::: ::: ::: METHODS ::: Attenuation Reflection-Fourier transformation infrared spectrometry with clustering analysis was used to the identification of Aaron's beard. ::: ::: ::: RESULTS ::: There were obvious differences in Aaron's beard. The results are consistent with that of morphologic study. ::: ::: ::: CONCLUSION ::: This method is rapid, simple and economical, and can be used to the quality control.