Chain Theories and Simplicial Abelian Group Spectra
نویسنده
چکیده
Two different definitions of a chain theory K∗ lead to the same class of derived homology theories h∗( ). On the category of CW pairs, these are those homology theories E∗ admitting a classifying simplicial abelian group spectrum E. So one has a functor from the category of chain theories into the category of simplicial abelian group spectra. 2000 Mathematics Subject Classification: 55U15, 55U10, 55P43.
منابع مشابه
Homology and homotopy in semi-abelian categories
The theory of abelian categories proved very useful, providing an ax-iomatic framework for homology and cohomology of modules over a ring (in particular, abelian groups) [5]. A similar framework has been lacking for non-abelian (co)homology, the subject of which includes the categories of groups and Lie algebras etc. The point of my thesis is that semi-abelian categories (in the sense of Janeli...
متن کاملR–torsion and linking numbers from simplicial abelian gauge theories
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R–torsion and linking numbers respectively. The new feature which makes this possible is the introduction of simplicial fields (cochains) associated with the dual triangulation of the ...
متن کاملAbelian gauge fields coupled to simplicial quantum gravity
We study the coupling of Abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge fields live on dual links. This is the correct formulation if we want to compare the effect of gauge fields on geometry with similar effects studied so far for scalar fields. It shows that gauge fields couple equally weakly to geometry as scalar fields, and it offers an understanding of the...
متن کاملAbelian gauge elds coupled to simplicialquantum
We study the coupling of abelian gauge theories to four-dimensional simplicial quantum gravity. The gauge elds live on dual links. This is the correct formulation if we want to compare the eeect of gauge elds on geometry with similar eeects studied so far for scalar elds. It shows that gauge elds couple equally weakly to geometry as scalar elds, and it ooers an understanding of the relation bet...
متن کاملHomotopy Theory of Simplicial Abelian Hopf Algebras
We examine the homotopy theory of simplicial graded abelian Hopf algebras over a prime field Fp, p > 0, proving that two very different notions of weak equivalence yield the same homotopy category. We then prove a splitting result for the Postnikov tower of such simplicial Hopf algebras. As an application, we show how to recover the homotopy groups of a simplicial Hopf algebra from its André-Qu...
متن کامل