470 research outputs found
A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type
Let (X,d,\mu) be a space of homogeneous type and E a UMD Banach space. Under
the assumption mu({x})=0 for all x in X, we prove a representation theorem for
singular integral operators on (X,d,mu) as a series of simple shifts and
rearrangements plus two paraproducts. This gives a T(1) Theorem in this
setting
Higher homotopy operations and cohomology
We explain how higher homotopy operations, defined topologically, may be
identified under mild assumptions with (the last of) the Dwyer-Kan-Smith
cohomological obstructions to rectifying homotopy-commutative diagrams.Comment: 28 page
Enclosings of Decompositions of Complete Multigraphs in -Edge-Connected -Factorizations
A decomposition of a multigraph is a partition of its edges into
subgraphs . It is called an -factorization if every
is -regular and spanning. If is a subgraph of , a
decomposition of is said to be enclosed in a decomposition of if, for
every , is a subgraph of .
Feghali and Johnson gave necessary and sufficient conditions for a given
decomposition of to be enclosed in some -edge-connected
-factorization of for some range of values for the parameters
, , , , : , and either ,
or and and , or and . We generalize
their result to every and . We also give some
sufficient conditions for enclosing a given decomposition of in
some -edge-connected -factorization of for every
and , where is a constant that depends only on ,
and~.Comment: 17 pages; fixed the proof of Theorem 1.4 and other minor change
Omega-categories and chain complexes
There are several ways to construct omega-categories from combinatorial
objects such as pasting schemes or parity complexes. We make these
constructions into a functor on a category of chain complexes with additional
structure, which we call augmented directed complexes. This functor from
augmented directed complexes to omega-categories has a left adjoint, and the
adjunction restricts to an equivalence on a category of augmented directed
complexes with good bases. The omega-categories equivalent to augmented
directed complexes with good bases include the omega-categories associated to
globes, simplexes and cubes; thus the morphisms between these omega-categories
are determined by morphisms between chain complexes. It follows that the entire
theory of omega-categories can be expressed in terms of chain complexes; in
particular we describe the biclosed monoidal structure on omega-categories and
calculate some internal homomorphism objects.Comment: 18 pages; as published, with minor changes from version
Moduli spaces of colored graphs
We introduce moduli spaces of colored graphs, defined as spaces of
non-degenerate metrics on certain families of edge-colored graphs. Apart from
fixing the rank and number of legs these families are determined by various
conditions on the coloring of their graphs. The motivation for this is to study
Feynman integrals in quantum field theory using the combinatorial structure of
these moduli spaces. Here a family of graphs is specified by the allowed
Feynman diagrams in a particular quantum field theory such as (massive) scalar
fields or quantum electrodynamics. The resulting spaces are cell complexes with
a rich and interesting combinatorial structure. We treat some examples in
detail and discuss their topological properties, connectivity and homology
groups
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