Asymptotics of the quantum invariants for surgeries on the figure 8 knot

We investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double contour integrals. These integral formulae allow us to propose a formula for the leading asymptotics of the invariants in the limit of large quantum level. We analyze this expression using the saddle point method. We construct a certain surjection from the set of stationary points for the relevant phase functions onto the space of conjugacy classes of nonabelian SL(2,C)-representations of the fundamental group of M and prove that the values of these phase functions at the relevant stationary points equal the classical Chern--Simons invariants of the corresponding flat SU(2)-connections. Our findings are in agreement with the asymptotic expansion conjecture. Moreover, we calculate the leading asymptotics of the colored Jones polynomial of the figure 8 knot following R. Kashaev. This leads to a slightly finer asymptotic description of the invariant than predicted by the volume conjecture of Kashaev and H. Murakami and J. Murakami.Comment: 70 pages, to appear in Journal of Knot Theory and Its Ramification

The rise and decline of extreme economic inequality in 20th century Japan: A literature review through the lens of institutional changes

 As economic inequality is rising in many countries around the world, the interest in how inequality has risen and declined in the past is being revived. Some researchers have seen modern history since the industrial revolution as a positive story of economic growth and technological progress that enhanced social development for all. Others have seen modern political economies as wrought with vicious cycles of inequality and social instability. This study investigates the rapid rise of economic inequality in Japan beginning in the 1880s and its equally dramatic fall in the 1930s. Using the World Income and Wealth Database’s new statistical data, I argue that Japan’s early economic development was characterised by highly inegalitarian institutions: taxation laws transfered resources from agriculture to urban centres for decades, corporate, financial and land properties were heavily concentrated in top income groups and rights-based organisations built by labour and women’s movements took time to gain national influence. The unequal strength of these institutions prevented economic growth from fostering inclusive development. Only with the outbreak of World War II were these institutions reformed during the collapse of the global economic system. This article thereby supports the development literature that draws clear distinctions between unequal growth and socio-economic equality tied to institutional change