This book provides a working knowledge of those parts of exterior differential forms,
differential geometry, algebraic and differential topology, Lie groups, vector bundles and
Chern forms that are essential for a deeper understanding of both classical and modern …

The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale
patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated
by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid …

Deals with an area of research that lies at the crossroads of mathematics and physics. The
material presented here rests primarily on the pioneering work of Vaughan Jones and
Edward Witten relating polynomial invariants of knots to a topological quantum field theory in …

KNOTS are usually categorized in terms of topological properties that are invariant under
changes in a knot's spatial configuration 1–4. Here we approach knot identification from a
different angle, by considering the properties of particular geometrical forms which we define …

In this survey article we discuss the origin, theory and applications of left-symmetric algebras
(LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have
introduced LSAs in mathematical physics (QFT and renormalization theory), where the name …

In this review article we discuss some of the applications of noncommutative geometry in
physics that are of recent interest, such as noncommutative many-body systems,
noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories …

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by
modifying the law of parallel displacement and using “standard” vectors. The field equations
are derived from a variational principle slightly different from that of Dirac and involving a …

" Geometry and Physics" addresses mathematicians wanting to understand modern physics,
and physicists wanting to learn geometry. It gives an introduction to modern quantum field
theory and related areas of theoretical high-energy physics from the perspective of …

A Galilei (Lorentz) structure on a manifold V is defined as a reduction of the bundle of linear
frames to a subbundle of frames invariant under the homogeneous Galilei (Lorentz) group.
Galileian or Newtonian and (general) relativistic theories are thus distinguished in a …

Recent interactions between the fields of geometry, classical and quantum dynamical
systems, and visualization of geometric objects such as curves and surfaces have led to the
observation that most concepts of surface theory and of the theory of integrable systems …