1,247 research outputs found
Brace algebras and the cohomology comparison theorem
The Gerstenhaber and Schack cohomology comparison theorem asserts that there
is a cochain equivalence between the Hochschild complex of a certain algebra
and the usual singular cochain complex of a space. We show that this comparison
theorem preserves the brace algebra structures. This result gives a structural
reason for the recent results establishing fine topological structures on the
Hochschild cohomology, and a simple way to derive them from the corresponding
properties of cochain complexes.Comment: Revised version of "The bar construction as a Hopf algebra", Dec.
200
A survey of subdivisions and local -vectors
The enumerative theory of simplicial subdivisions (triangulations) of
simplicial complexes was developed by Stanley in order to understand the effect
of such subdivisions on the -vector of a simplicial complex. A key role
there is played by the concept of a local -vector. This paper surveys some
of the highlights of this theory and some recent developments, concerning
subdivisions of flag homology spheres and their -vectors. Several
interesting examples and open problems are discussed.Comment: 13 pages, 3 figures; minor changes and update
Lattice Topological Field Theory on Non-Orientable Surfaces
The lattice definition of the two-dimensional topological quantum field
theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is
generalized to arbitrary (not necessarily orientable) compact surfaces. It is
shown that there is a one-to-one correspondence between real associative
-algebras and the topological state sum invariants defined on such surfaces.
The partition and -point functions on all two-dimensional surfaces
(connected sums of the Klein bottle or projective plane and -tori) are
defined and computed for arbitrary -algebras in general, and for the the
group ring of discrete groups , in particular.Comment: Corrected Latex file, 39 pages, 28 figures available upon reques
Difference Problems and Differential Problems
We state some elementary problems concerning the relation between difference
calculus and differential calculus, and we try to convince the reader that, in
spite of the simplicity of the statements, a solution of these problems would
be a significant contribution to the understanding of the foundations of
differential and integral calculus
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