" Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of
variations. Many of the techniques developed have played key roles in geometry and partial …

This graduate level text describes in a unified fashion the statistical mechanics of random
walks, random surfaces and random higher dimensional manifolds with an emphasis on the …

Perturbative and nonperturbative aspects of complex Chern–Simons theory - IOPscience Skip
to content IOP Science home Accessibility Help Search Journals Journals list Browse more …

The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order
to classify compact 3-manifolds by means of a canonical decomposition along essential …

The authors of this article believe there is or should be a research area appropriately
referred to as computational topology. Its agenda includes the identification and …

We show that the problem of deciding whether a polygonal knot in a closed three-
dimensional manifold bounds a surface of genus at most $ g $ is NP-complete. We also …

Let EMBEDk→ d be the following algorithmic problem: Given a finite simplicial complex K of
dimension at most k, does there exist a (piecewise linear) embedding of K into Rd? Known …

We give a topological characterisation of alternating knot exteriors based on the presence of
special spanning surfaces. This shows that being alternating is a topological property of the …

We prove two results, one semi-historical and the other new. The semi-historical result,
which goes back to Thurston and Riley, is that the geometrization theorem implies that there …

We prove that the fundamental group of any integer homology 3-sphere different from the 3-
sphere admits irreducible representations of its fundamental group in SL (2, C). For …