Invariants of piecewise-linear 3-manifolds
نویسندگان
چکیده
منابع مشابه
Invariants of Piecewise - Linear 3 - Manifolds
The purpose of this paper is to present an algebraic framework for constructing invariants of closed oriented 3-manifolds. The construction is in the spirit of topological field theory and the invariant is calculated from a triangulation of the 3-manifold. The data for the construction of the invariant is a tensor category with a condition on the duals, which we have called a spherical category...
متن کاملInvariants of 3 - Manifolds
The ju-invariant fi(M) of an oriented Z2 -homology 3-sphere M is defined by Hirzebruch in [8], using Rohlin's Theorem [13], to be the mod 16 reduction of the signature of a framed manifold W with M = dW. In this paper we give a formula for p(M) by studying M as a branched dihedral covering space of S 3 . Hilden [7] and Montesinos [9] have independently shown that every closed orientable 3-manif...
متن کاملSpaces of Piecewise Linear Manifolds
In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
متن کاملSpaces of Piecewise Linear Manifolds
In this thesis we introduce a ∆-set Ψ d (R )• which we regard as the piecewise linear analogue of the space Ψd(R ) of smooth d-dimensional submanifolds in R introduced by Galatius in [4]. Using Ψ d (R )• we define a bi-∆-set Cd(R )•,• whose geometric realization BC d (R ) = ∥∥Cd(RN )•,•∥∥ should be interpreted as the PL version of the classifying space of the category of smooth d-dimensional co...
متن کاملQuantum Invariants of 3-manifolds
The idea to derive topological invariants of smooth manifolds from partitions functions of certain action functionals was suggested by A. Schwarz (1978) and highlighted by E. Witten (1988). Witten interpreted the Jones polynomial of links in the 3-sphere S as a partition function of the Chern-Simons field theory. Witten conjectured the existence of mathematically defined topological invariants ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1996
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-96-01660-1