pressure gauges
gauge fields knots and gravity
this is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity . the book begins with a rapid course on manifolds and differential forms emphasizing how these provide a proper language for formulating maxwells equations on arbitrary spacetimes . the authors then introduce vector bundles connections and curvature in order to generalize maxwell theory to the yang mills equations . the relation of gauge theory to the newly discovered knot invariants such as the jones polynomial is sketched . riemannian geometry is then introduced in order to describe einsteins equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory .