51,032 research outputs found
A complete solution to the infinite Oberwolfach problem
Let be a -regular graph of order . The Oberwolfach problem,
, asks for a -factorization of the complete graph on vertices in
which each -factor is isomorphic to . In this paper, we give a complete
solution to the Oberwolfach problem over infinite complete graphs, proving the
existence of solutions that are regular under the action of a given involution
free group . We will also consider the same problem in the more general
contest of graphs that are spanning subgraphs of an infinite complete graph
and we provide a solution when is locally finite. Moreover, we
characterize the infinite subgraphs of such that there exists a
solution to containing a solution to
Schwartz functions on Nash manifolds
In this paper we extend the notions of Schwartz functions, tempered functions
and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic)
manifolds. We reprove for this case classically known properties of Schwartz
functions on and build some additional tools which are important in
representation theory.Comment: 35 pages, LaTex. v3:minor changes + reference to results of duClou
Complete algebraic vector fields on affine surfaces
Let \AAutH (X) be the subgroup of the group \AutH (X) of holomorphic
automorphisms of a normal affine algebraic surface generated by elements of
flows associated with complete algebraic vector fields. Our main result is a
classification of all normal affine algebraic surfaces quasi-homogeneous
under \AAutH (X) in terms of the dual graphs of the boundaries \bX \setminus
X of their SNC-completions \bX.Comment: 44 page
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