

Lecture note 31/2006
Topics in Physical Mathematics: Geometric Topology and Field Theory
Kishore Marathe
Contact the author: Please use for correspondence this email.
Submission date: 03. Aug. 2006
Pages: 76
published as:
Marathe, K. B.: Topics in physical mathematics
London : Springer, 2010. - XXII, 442 p.
ISBN 978-1-84882-938-1 - ISBN 978-1-84882-939-8
Bibtex
MSC-Numbers: 57R56, 81T13, 81T30, 83C05
PACS-Numbers: 11.15.Tk, 11.25.Tq, 11.30.Pb
Keywords and phrases: geometric topology, field theory, knot invariants
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Abstract:
In recent years the interaction between geometic topology
and classical and quantum field theories has attracted
a great deal of attention from both the mathematicians
and physicists.
We discuss some topics from low dimensional topology
where this has led to new viewpoints as well as new
results. They include categorification of knot polynomials
and a special case of the gauge theory to string
theory correspondence
in the Euclidean version of the theories,
where exact results are available.
We show how the Witten-Reshetikhin-Turaev invariant in
SU(n) Chern-Simons theory on is related via
conifold transition to the all-genus
generating function of the topological string
amplitudes on a Calabi-Yau manifold. This result can be
thought of as an interpretation of TQFT as
TQG (Topological Quantum Gravity). A brief discussion of
Perelman's work on the geometrization conjecture and its
relation to gravity is also included.