Characteristic forms and geometric invariants

  title={Characteristic forms and geometric invariants},
  author={Shiing-shen Chern and James Simons},
  journal={Annals of Mathematics},
The Autodidactic Universe
An approach to cosmology in which the Universe learns its own physical laws by exploring a landscape of possible laws by discovering maps that put each of these matrix models in correspondence with both a gauge/gravity theory and a mathematical model of a learning machine, such as a deep recurrent, cyclic neural network.
Distinguishing Mutant knots
Anomalies in the space of coupling constants and their dynamical applications I
It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincaré symmetry) to background gauge fields
Search for black holes and sphalerons in high-multiplicity final states in proton-proton collisions at $\sqrt{s} =$ 13 TeV
A search in energetic, high-multiplicity final states for evidence of physics beyond the standard model, such as black holes, string balls, and electroweak sphalerons, is presented. The data sample
Aspects of particle cosmology with an emphasis on baryogenesis
Cosmology provides some compelling reasons to expect physics beyond the Standard Model on top of theoretical concerns such as the hierarchy problem and grand unification. In this thesis I explore
The Geometry of Loop Spaces II: Characteristic Classes
Towards ℛ-matrix construction of Khovanov-Rozansky polynomials I. Primary T-deformation of HOMFLY
A bstractWe elaborate on the simple alternative [1] to the matrix-factorization construction of Khovanov-Rozansky (KR) polynomials for arbitrary knots and links in the fundamental representation of
Chern-Weil theory for certain infinite-dimensional Lie groups
Chern–Weil and Chern–Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding
Colored HOMFLY Polynomials as Multiple Sums over Paths or Standard Young Tableaux
If a knot is represented by an -strand braid, then HOMFLY polynomial in representation is a sum over characters in all representations . Coefficients in this sum are traces of products of quantum
Colored knot amplitudes and Hall-Littlewood polynomials
The amplitudes of refined Chern-Simons (CS) theory, colored by antisymmetric (or symmetric) representations, conjecturally generate the Lambda^r- (or S^r-) colored triply graded homology of (n,m)


Some cohomology classes in principal fiber bundles and their application to riemannian geometry.
  • S. Chern, J. Simons
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1971
Some new global invariants of a fiber bundle with a connection are cohomology classes in the principal fiber bundle that are defined when certain characteristic curvature forms vanish and give necessary conditions for conformal immersion of a riemannian manifold in euclidean space.
Foundation of Differential Geometry
  • Vol. I, II, Interscience
  • 1969
La cohomologie mod 2 de certains espaces homogènes
Ce travail est consacr6 ~ l'dtude de la cohomologie mod 2 de quelques espaces homog~nes ou fibrds principaux des groupes orthogonaux, pour la plupart classiques. Comme dans [2], nous utilisons
On Conformally-Flat Spaces in the Large
Non-Riemannian Geometry
Asymmetric connections Symmetric connections Projective geometry of paths The geometry of subspaces Bibliography.