arXiv subjects
Publications and source records attributed to Pierre Vogel.
We introduce a new notion of regularity for rings and exact categories and we show important results in algebraic K-theory. In particular we prove a strong vanishing theorem for Nil groups and give an explicit class of groups, much bigger than Waldhausen's class Cl, such that every group in this class has trivial Whitehead groups.
In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a localization functor corresponding to this class of homology equivalences and we give a characterization of local objects in terms of homotopy groups.
In this paper, we extend Waldhausen's results on algebraic K-theory of generalized free produts in a more general setting and we give some properties of the Nil functors. As a consequence, we get new groups with trivial Whitehead groups.
The purpose of this paper is to give a complete description of the Cohn localization of the augmentation map $Z[G]\rightarrow Z$ when $G$ is any finite group.
In this paper we prove that every Khovanov homology associated to a Frobenius algebra of rank $2$ can be modified in such a way as to produce a TQFT on oriented links, that is a monoidal functor from the category of cobordisms of oriented links to the homotopy category of complexes.