Three Books on the Scottish Sixties

Discusses three recent books about Scottish culture in the 1960s: a collection of documents and interviews, The International Writers\u27 Conference Revisited, ed. Bartie and Bell; a collection of essays, The Scottish Sixties, ed. Bell and Gunn; and a monograph, The Edinburgh Festivals, by Angela Bartie

Involutory Hopf algebras and 3-manifold invariants

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the invariant counts homomorphisms from the fundamental group of the manifold to $G$. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and contractions of the structure tensors of the algebra. We show that every formal expression involving these tensors corresponds to a unique 3-manifold modulo a well-understood equivalence. This raises the possibility of an algorithm which can determine whether two given 3-manifolds are homeomorphic.Comment: Figure 4 is missin

What is a virtual link?

Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a link L in S X I, a thickened, compact, oriented surface S, such that the link complement (S X I) - L has no essential vertical cylinder.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-20.abs.htm

Collider Searches for Extra Dimensions

Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. Until the start of the LHC in a few years, the Tevatron will remain the key player in this quest. In this paper, we review the most recent results from the Tevatron on searches for large, 1/TeV-size, and Randall-Sundrum extra spatial dimensions, which have reached a new level of sensitivity and currently probe the parameter space beyond the existing constraints. While no evidence for the existence of extra dimensions has been found so far, an exciting discovery might be just steps away.Comment: To appear in Proceedings of SLAC Summer Institute, 2004. An extended version of the talk given on behalf of the CDF and D0 Collaboration