5,314 research outputs found
A Combintorial Proof of the Sum of q-Cubes
We give a combinatorial proof of a q-analogue of the classical formula for the sum of cubes
Cubulations, immersions, mappability and a problem of Habegger
The aim of this paper (inspired from a problem of Habegger) is to describe
the set of cubical decompositions of compact manifolds mod out by a set of
combinatorial moves analogous to the bistellar moves considered by Pachner,
which we call bubble moves. One constructs a surjection from this set onto the
the bordism group of codimension one immersions in the manifold. The connected
sums of manifolds and immersions induce multiplicative structures which are
respected by this surjection. We prove that those cubulations which map
combinatorially into the standard decomposition of for large enough
(called mappable), are equivalent. Finally we classify the cubulations of
the 2-sphere.Comment: Revised version, Ann.Sci.Ecole Norm. Sup. (to appear
A chain morphism for Adams operations on rational algebraic K-theory
For any regular noetherian scheme X and every k>0, we define a chain morphism
between two chain complexes whose homology with rational coefficients is
isomorphic to the algebraic K-groups of X tensored by the field of rational
numbers. It is shown that these morphisms induce in homology the Adams
operations defined by Gillet and Soule or the ones defined by Grayson.Comment: 40 page
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