Classification of Links Up to 0-Solvability

The $n$-solvable filtration of the $m$-component smooth (string) link concordance group, $$\dots \subset \mathcal{F}^m_{n+1} \subset \mathcal{F}^m_{n.5} \subset \mathcal{F}^m_n \dots \subset \mathcal{F}^m_1 \subset \mathcal{F}^m_{0.5} \subset \mathcal{F}^m_0 \subset \mathcal{F}^m_{-0.5} \subset \mathcal{C}^m,$$ as defined by Cochran, Orr, and Teichner, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. The focus of this paper is to give a characterization of the set of 0-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric classification of $\mathbb{L}_0^m$, the set of links up to 0-solve equivalence. We show that $\mathbb{L}_0^m$ has a group structure isomorphic to the quotient $\mathcal{F}_{-0.5}/\mathcal{F}_0$ of concordance classes of string links and classify this group, showing that $$\mathbb{L}_0^m \cong \mathcal{F}_{-0.5}^m/\mathcal{F}_0^m \cong \mathbb{Z}_2^m \oplus \mathbb{Z}^{m \choose 3} \oplus \mathbb{Z}_2^{m \choose 2}.$$ Finally, using results of Conant, Schneiderman, and Teichner, we show that 0-solvable links are precisely the links that bound class 2 gropes and support order 2 Whitney towers in the 4-ball.Comment: 34 page

Why are the Children Dying?: Mixed-Race Children in Chang-rae Lee’s First Five Novels

The mixed-race children in each of Lee’s first five novels constitute an overarching set of symbols, reflecting, at first, society’s intolerance of miscegenation and its resulting mixed offspring, as demonstrated in the dysfunctional behaviors of the parent(s) (or society) and the death or disappearance of the mixed-race child. Then, later in the novel, a second mixed-race child’s birth, or its impending birth, signifies an acquired racial awareness on the part of the parent(s) and an overcoming of trauma that leads to hope for a more tolerant and understanding social environment for the mixed-race child

Cosimo de’ Medici: Patron, Banker, and Pater Patriae

This paper investigates the connection between art, money, and power in the life of Cosimo de\u27 Medici. It discusses several important art works commissioned by Cosimo, including the Medici Palace and Donatello\u27s bronze David. It also examines Cosimo\u27s life as a businessman and a political figure

Preaching Mark

Reid, Robert Stephen. Preaching Mark. St Louis: Chalice Press, 1999

BEES. THEIR VISION, CHEMICAL SENSES, AND LANGUAGE by Karl von Frisch

BEES. THEIR VISION, CHEMICAL SENSES, AND LANGUAGE. Karl von Frisch, the University of Munich. Revised edition. Cornell University Press, Ithaca, New York and London. 157 pages. $7.50 ( 3.50), paperback$2.45

The Gospel of John in the light of the Old Testament

Westermann, Claus. The Gospel of John in the light of the Old Testament. Peabody, Mass: Hendrickson, 1998