IN THE 1980s the topology of low dimensional manifolds has experienced the most
remarkable intervention of ideas developed in rather distant areas of mathematics. In the 4 …

The complexity of a 3-manifold is a whole number which measures how complicated a
combinatorial description of the manifold must be. It has many pleasant properties, among …

Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and JHC
Whitehead. Much work in this area has been done since then, and this book considers the …

Two transformations, called elementary, are defined for special spines, and it is shown that
any one special spine of a 3-manifold can be obtained from any other by a sequence of …

In [1] GB Casler introduced 2-dimensional standard polyhedra and proved that any 3-
manifold with boundary has a standard spine (cf. also [9]) and any such a spine uniquely …

In this paper we provide a presentation for compact oriented 3-manifolds with non-empty
boundary up to orientation-preserving homeomorphism via a calculus on suitable finite …

As has been observed by Morse\cite {Mo}, any generic vector field $ v $ on a compact
smooth manifold $ X $ with boundary gives rise to a stratification of the boundary $\d X $ by …

In this paper the new concept of an n-algebra is introduced, which embodies the
combinatorial properties of an n-tensor, in an analogous manner to the way ordinary …

A topological quantum field theory (TQFT) is an, almost, metric independent quantum field
theory that gives rise to topological invariants of the background manifold. The best known …

The method of Turaev and Viro is generalized to construct state-sum invariants of 3-
manifolds using an artinian semisimple tortile category as initial data. In the first two sections …