

Preprint 45/2009
Geometric Topology and Field Theory on 3-Manifolds
Kishore Marathe
Contact the author: Please use for correspondence this email.
Submission date: 27. Jul. 2009
Pages: 63
published in: The mathematics of knots : theory and application / M. Banagl ... (eds.)
Heidelberg [u.a.] : Springer, 2011. - P. 199 - 256
(Contributions in mathematical and computational sciences ; 1)
DOI number (of the published article): 10.1007/978-3-642-15637-3_8
Bibtex
MSC-Numbers: 81T13, 81T45, 53C07
Keywords and phrases: geometric topology, Field theories, invariants of 3-manifolds
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Abstract:
In recent years the interaction between geometric topology
and classical and quantum field theories has attracted
a great deal of attention from both the mathematicians
and physicists. This interaction has been especially
fruitful in low dimensional topology. In this article
We discuss some topics from the geometric topology of
3-manifolds with or without links
where this has led to new viewpoints as well as new
results. They include in addition to the early work of
Witten, Casson, Bott, Taubes and others, the categorification
of knot polynomials by Khovanov. Rozansky, Bar-Natan and
Garofouladis
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.