We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3)-TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given.
Abstract. We consider collections of surfaces {F'¡} smoothly embedded, except for a finite number of isolated singularities, self-intersections, and mutual intersections, in a 4-manifold M. A small 3-sphere about each exceptional point will intersect these surfaces in a link. If [F¡] G H2(M) are linearly dependent modulo a prime power, we find lower bounds for 2 genus (/)■) in terms of the [F¡], and invariants of the links that describe the exceptional points.0. Introduction. The following special case of our main theorem is easy to state.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.