29,829 research outputs found
Diffeological Clifford algebras and pseudo-bundles of Clifford modules
We consider the diffeological version of the Clifford algebra of a
(diffeological) finite-dimensional vector space; we start by commenting on the
notion of a diffeological algebra (which is the expected analogue of the usual
one) and that of a diffeological module (also an expected counterpart of the
usual notion). After considering the natural diffeology of the Clifford
algebra, and its expected properties, we turn to our main interest, which is
constructing pseudo-bundles of diffeological Clifford algebras and those of
diffeological Clifford modules, by means of the procedure called diffeological
gluing. The paper has a significant expository portion, regarding mostly
diffeological algebras and diffeological vector pseudo-bundles.Comment: 35 pages; exposition improved, an example adde
Diffeological vector pseudo-bundles
We consider a diffeological counterpart of the notion of a vector bundle (we
call this counterpart a pseudo-bundle, although in the other works it is called
differently; among the existing terms there are a "regular vector bundle" of
Vincent and "diffeological vector space over X" of Christensen-Wu). The main
difference of the diffeological version is that (for reasons stemming from the
independent appearance of this concept elsewhere), diffeological vector
pseudo-bundles may easily not be locally trivial (and we provide various
examples of such, including those where the underlying topological bundle is
even trivial). Since this precludes using local trivializations to carry out
many typical constructions done with vector bundles (but not the existence of
constructions themselves), we consider the notion of diffeological gluing of
pseudo-bundles, which, albeit with various limitations that we indicate,
provides when applicable a substitute for said local trivializations. We
quickly discuss the interactions between the operation of gluing and typical
operations on vector bundles (direct sum, tensor product, taking duals) and
then consider the notion of a pseudo-metric on a diffeological vector
pseudo-bundle.Comment: 29 pages, no figure
Groups of tree automorphisms as diffeological groups
We consider certain groups of tree automorphisms as so-called diffeological
groups. The notion of diffeology, due to Souriau, allows to endow non-manifold
topological spaces, such as regular trees that we look at, with a kind of a
differentiable structure that in many ways is close to that of a smooth
manifold; a suitable notion of a diffeological group follows. We first study
the question of what kind of a diffeological structure is the most natural to
put on a regular tree in a way that the underlying topology be the standard one
of the tree. We then proceed to consider the group of all automorphisms of the
tree as a diffeological space, with respect to the functional diffeology,
showing that this diffeology is actually the discrete one, the fact that
therefore is true for its subgroups as well.Comment: 11 pages, 1 figure; rather minor changes with respect to the previous
versio
Some applications of p-adic uniformization to algebraic dynamics
This is not a research paper, but a survey submitted to a proceedings volume.Comment: 21 pages, LaTe
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