Point-pushing in 3-manifolds

We study the Birman exact sequence for compact 3-manifolds.Comment: 33 pages, 1 figure. v2: Incorrect Lemma 6.21 replaced. Corollary 7.4 (now 7.5) strengthened. Other small changes in exposition. An alternative, more algebraic, proof of Theorem 7.2 (with less exposition) is given in arXiv:1404.368

The Kakimizu complex of a connected sum of links

We show that |MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R} when $L_1$ and $L_2$ are any non-split and non-fibred links. Here $MS(L)$ denotes the Kakimizu complex of a link $L$, which records the taut Seifert surfaces for $L$. We also show that the analogous result holds if we study incompressible Seifert surfaces instead of taut ones.Comment: 23 pages, 8 figures. This result has been proved independently by Bassem Saa

The Birman exact sequence for 3-manifolds

We study the Birman exact sequence for compact $3$--manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping class group of the submanifold obtained by deleting an interior point. This covers both orientable manifolds and non-orientable ones.Comment: 30 pages, no figures. v2: Major re-write following referee suggestions. To appear in Bull. Lond. Math. Soc.; v1: This paper gives an alternative, more algebraic, proof of the main result of arXiv:1310.7884 (with less exposition

On links with locally infinite {K}akimizu complexes

We show that the Kakimizu complex of a knot may be locally infinite, answering a question of Przytycki--Schultens. We then prove that if a link $L$ only has connected Seifert surfaces and has a locally infinite Kakimizu complex then $L$ is a satellite of either a torus knot, a cable knot or a connected sum, with winding number 0.Comment: 9 pages, 5 figures; v2 minor has minor changes incorporating referee's comments. To appear in Algebraic & Geometric Topolog

Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial

We give a geometric proof of the following result of Juhasz. \emph{Let $a_g$ be the leading coefficient of the Alexander polynomial of an alternating knot $K$. If $|a_g|<4$ then $K$ has a unique minimal genus Seifert surface.} In doing so, we are able to generalise the result, replacing `minimal genus' with `incompressible' and `alternating' with `homogeneous'. We also examine the implications of our proof for alternating links in general.Comment: 37 pages, 28 figures; v2 Main results generalised from alternating links to homogeneous links. Title change

Examining the Protective Effect of Ethnic Identity on Drug Attitudes and Use Among a Diverse Youth Population

Ethnic identity is an important buffer against drug use among minority youth. However, limited work has examined pathways through which ethnic identity mitigates risk. School-aged youth (N = 34,708; 52 % female) of diverse backgrounds (i.e., African American (n = 5333), Asian (n = 392), Hispanic (n = 662), Multiracial (n = 2129), Native American (n = 474), and White (n = 25718) in grades 4–12 provided data on ethnic identity, drug attitudes, and drug use. After controlling for gender and grade, higher ethnic identity was associated with lower past month drug use for African American, Hispanic, and Multiracial youth. Conversely, high ethnic identity was associated with increased risk for White youth. An indirect pathway between ethnic identity, drug attitudes, and drug use was also found for African American, Hispanic, and Asian youth. Among White youth the path model was also significant, but in the opposite direction. These findings confirm the importance of ethnic identity for most minority youth. Further research is needed to better understand the association between ethnic identity and drug use for Multiracial and Hispanic youth, best ways to facilitate healthy ethnic identity development for minority youth, and how to moderate the risk of identity development for White youth