Equivariant isomorphisms of Ext and Tor modules

Notes on Tor and Ext

1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...

Ext, Tor and the Uct

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Some Common Tor and Ext Groups

We compute all the groups G⊗H, Tor(G, H), Hom(G, H), and Ext(G, H), where G and H can be any of the groups Z (the integers), Z/n = Z/nZ (the integers mod n), or Q (the rationals). All but one are reasonably accessible. Because all these functors are biadditive, these cases suffice to handle any finitely generated groups G and H. The emphasis here is on computation, not on the abstract definitio...

Equivariant Cohomology and Analytic Descriptions of Ring Isomorphisms

In this paper we consider a class of connected closed G-manifolds with a non-empty finite fixed point set, each M of which is totally non-homologous to zero in MG (or G-equivariantly formal), where G = Z2. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a G-manifold in terms of algebra, so that we can obtain analytic descriptions of ...