Branched covers of quasipositive links and L-spaces

Let $L$ be a oriented link such that $\Sigma_n(L)$, the $n$-fold cyclic cover of $S^3$ branched over $L$, is an L-space for some $n \geq 2$. We show that if either $L$ is a strongly quasipositive link other than one with Alexander polynomial a multiple of $(t-1)^{2g(L) + (|L|-1)}$, or $L$ is a quasipositive link other than one with Alexander polynomial divisible by $(t-1)^{2g_4(L) + (|L|-1)}$, then there is an integer $n(L)$, determined by the Alexander polynomial of $L$ in the first case and the Alexander polynomial of $L$ and the smooth $4$-genus of $L$, $g_4(L)$, in the second, such that $n \leq n(L)$. If $K$ is a strongly quasipositive knot with monic Alexander polynomial such as an L-space knot, we show that $\Sigma_n(K)$ is not an L-space for $n \geq 6$, and that the Alexander polynomial of $K$ is a non-trivial product of cyclotomic polynomials if $\Sigma_n(K)$ is an L-space for some $n = 2, 3, 4, 5$. Our results allow us to calculate the smooth and topological 4-ball genera of, for instance, quasi-alternating quasipositive links. They also allow us to classify strongly quasipositive alternating links and $3$-strand pretzel links.Comment: 49 pages, 7 figures, minor corrections and improved exposition, accepted for publication by the Journal of Topolog

Reducible And Finite Dehn Fillings

We show that the distance between a finite filling slope and a reducible filling slope on the boundary of a hyperbolic knot manifold is at most one.Comment: 17 pages, 11 figure

On definite strongly quasipositive links and L-space branched covers

We investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched cover. In particular, we show that if $\delta_n = \sigma_1 \sigma_2 \ldots \sigma_{n-1}$ is the dual Garside element and $b = \delta_n^k P \in B_n$ is a strongly quasipositive braid whose braid closure $\widehat b$ is definite, then $k \geq 2$ implies that $\widehat b$ is one of the torus links $T(2, q), T(3,4), T(3,5)$ or pretzel links $P(-2, 2, m), P(-2,3,4)$. Applying Theorem 1.1 of our previous paper we deduce that if one of the standard cyclic branched covers of $\widehat b$ is an L-space, then $\widehat b$ is one of these links. We show by example that there are strongly quasipositive braids $\delta_n P$ whose closures are definite but not one of these torus or pretzel links. We also determine the family of definite strongly quasipositive $3$-braids and show that their closures coincide with the family of strongly quasipositive $3$-braids with an L-space branched cover.Comment: 62 pages, minor revisions, accepted for publication in Adv. Mat

The relationship between national well-being and xenophobia in a divided society: The case of South Africa

Personal well-being surveys have increased their coverage on the African continent in recent years, but detailed research on subjective national wellbeing is less  common. The link between national well-being and xenophobic sentiments has not been adequately tested in an African context. In order to better understand (and correspondingly counter) xenophobic sentiments in sub-Saharan Africa, this article tests the correlation of National Well-being Index (NWI) with attitudes towards immigrants in a sub-Saharan country. South Africa was chosen as the research site for this study and data were used from the 2012 South African Social Attitudes Survey (SASAS), a nationally representative opinion poll of 2 521 respondents. In 2012 the six items that constitute the NWI were included in this survey, measuring public evaluations of the country’s economic, natural, governmental, social and security environment. This allowed the construction of the NWI, a composite score that provides a more precise measurement of sociotropic concerns. The findings of this study show that, even when controlling for individual well-being and socio-economic status, the NWI had a statistically significant relationship with attitudes towards immigrants. The lower the reported NWI, the more likely an individual will be to believe negative stereotypes about immigrants. This suggests the importance of studying and measuring subjective national well-being on the African continent.Keywords: Immigration, national well-being, National Well-being Index, South Africa, xenophobi

The Political Power of Social Media Revisited

This paper revisits an article published in Foreign Affairs magazine titled “The Political Power of Social Media” (Shirky, 2011) in light of the explosion in the use of social media for political purposes subsequent to its publication. It examines how social media have exerted and will continue to exert power to effect political and social change, focusing on five specific functions – raising community awareness, framing issues, engaging with mass media, stimulating and organizing protest, and obtaining resources

The Returns to Lobbying: Evidence from Local Governments in the Age of Earmarks

The federal government transfers considerable sums to local governments in the form of intergovernmental grants. With the exception of health and welfare programs, most intergovernmental grants to local governments are classified as discretionary spending. In its annual appropriations process, Congress decides how funding for discretionary spending will be broken up among the various agencies, but more detailed decisions about specific uses of funds are left to the executive branch