60,374 research outputs found
Surgery and involutions on 4-manifolds
We prove that the canonical 4-dimensional surgery problems can be solved
after passing to a double cover. This contrasts the long-standing conjecture
about the validity of the topological surgery theorem for arbitrary fundamental
groups (without passing to a cover). As a corollary, the surgery conjecture is
reformulated in terms of the existence of free involutions on a certain class
of 4-manifolds. We consider this question and analyze its relation to the
A,B-slice problem.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-70.abs.htm
Proper twin-triangular Ga-actions on A^4 are translations
An additive group action on an affine 3 -space over a complex Dedekind domain
A is said to be twin-triangular if it is generated by a locally nilpotent
derivation of A[y,z,t] of the form rd/dy+p(y)d/dz + q(y)d/dt, where r belongs
to A and p,q belong to A[y] . We show that these actions are translations if
and only if they are proper. Our approach avoids the computation of rings of
invariants and focuses more on the nature of geometric quotients for such
actions
Applications of Topological *-Algebras of Unbounded Operators
In this paper we discuss some physical applications of topological *-algebras
of unbounded operators. Our first example is a simple system of free bosons.
Then we analyze different models which are related to this one. We also discuss
the time evolution of two interacting models of matter and bosons. We show that
for all these systems it is possible to build up a common framework where the
thermodynamical limit of the algebraic dynamics can be conveniently studied and
obtained.Comment: Latex file, no figur
Deformation of string topology into homotopy skein modules
Relations between the string topology of Chas and Sullivan and the homotopy
skein modules of Hoste and Przytycki are studied. This provides new insight
into the structure of homotopy skein modules and their meaning in the framework
of quantum topology. Our results can be considered as weak extensions to all
orientable 3-manifolds of classical results by Turaev and Goldman concerning
intersection and skein theory on oriented surfaces.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-34.abs.htm
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