ترغب بنشر مسار تعليمي؟ اضغط هنا

Landweber exact formal group laws and smooth cohomology theories

116   0   0.0 ( 0 )
 نشر من قبل Thomas Schick
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English
 تأليف Ulrich Bunke




اسأل ChatGPT حول البحث

The main aim of this paper is the construction of a smooth (sometimes called differential) extension hat{MU} of the cohomology theory complex cobordism MU, using cycles for hat{MU}(M) which are essentially proper maps Wto M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of Wto M. Crucial is that this model allows the construction of a product structure and of pushdown maps for this smooth extension of MU, which have all the expected properties. Moreover, we show, using the Landweber exact functor principle, that hat{R}(M):=hat{MU}(M)otimes_{MU^*}R defines a multiplicative smooth extension of R(M):=MU(M)otimes_{MU^*}R whenever R is a Landweber exact MU*-module. An example for this construction is a new way to define a multiplicative smooth K-theory.



قيم البحث

اقرأ أيضاً

136 - Sebastian Thomas 2009
We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M.
116 - Paul G. Goerss 2009
I discuss the problem of realizing families of complex orientable homology theories as families of commutative ring spectra, including a recent result of Jacob Lurie emphasizing the role of p-divisible groups.
We use (non-)additive sheaves to introduce an (absolute) notion of Hochschild cohomology for exact categories as Exts in a suitable bisheaf category. We compare our approach to various definitions present in the literature.
142 - Paolo Piazza 2013
The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new ind ex theorems for the signature operator on Galois coverings with boundary. These are of independent interest and form the second main theme of the paper. The main technical novelty is the use of large scale index theory for Dirac type operators that are perturbed by lower order operators.
Suppose k is a field of characteristic 2, and $n,mgeq 4$ powers of 2. Then the $A_infty$-structure of the group cohomology algebras $H^*(C_n,k)$ and $(H^*(C_m,k)$ are well known. We give results characterizing an $A_infty$-structure on $H^*(C_ntimes C_m,k)$ including limits on non-vanishing low-arity operations and an infinite family of non-vanishing higher operations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا