اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRO(S^1)-graded TR-groups of F_p, Z and ell
135
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give an algorithm for calculating the RO(S^1)-graded TR-groups of F_p, completing the calculation started by the second author. We also calculate the RO(S^1)-graded TR-groups of Z with mod p coefficients and of the Adams summand ell of connective complex K-theory with V(1)-coefficients. Some of these calculations are used elsewhere to compute the algebraic K-theory of certain Z-algebras.
قيم البحث
اقرأ أيضاً
The main result of this paper is the computation of TR^n_{alpha}(F_p;p) for alpha in R(S^1). These R(S^1)-graded TR-groups are the equivariant homotopy groups naturally associated to the S^1-spectrum THH(F_p), the topological Hochschild S^1-spectrum.
This computation, which extends a partial result of Hesselholt and Madsen, provides the first example of the R(S^1)-graded TR-groups of a ring. These groups arise in algebraic K-theory computations, and are particularly important to the understanding of the algebraic K-theory of non-regular schemes.
We completely calculate the $RO(G)$-graded coefficients of ordinary equivariant cohomology where $G$ is the dihedral group of order $2p$ for a prime $p>2$ both with constant and Burnside ring coefficients. The authors first proved it for $p=3$ and th
en the second author generalized it to arbitrary $p$. These are the first such calculations for a non-abelian group.
This thesis consists of two main parts. In the second part, we recall how a description of local coefficients that Eilenberg introduced in the 1940s leads to spectral sequences for the computation of homology and cohomology with local coefficients. W
e then show how to construct new equivariant analogues of these spectral sequences for RO(G)-graded Bredon homology and cohomology. Finally, we use these spectral sequences to complete a sample calculation, in which we use the equivariant Serre spectral sequence and the equivariant cohomology of complex projective spaces to compute the cohomology of the equivariant classifying space B_Cp O(2). However, to complete this sample computation, we need to know the cohomology of complex projective space. This calculation was done in a 1988 paper by Gaunce Lewis, but relies on a theorem whose proof as given was incorrect. We spend the first part of this thesis providing a correct proof and summarizing the results of Lewiss paper.
We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, K_G on the category of proper G-CW complexes. We then
study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable hightest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto K_G^*(EG), where $EG$ is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute K_G^*(EG) for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E_{10}.
We study the homotopy type of the space of the unitary group $operatorname{U}_1(C^ast_u(|mathbb{Z}^n|))$ of the uniform Roe algebra $C^ast_u(|mathbb{Z}^n|)$ of $mathbb{Z}^n$. We show that the stabilizing map $operatorname{U}_1(C^ast_u(|mathbb{Z}^n|))
tooperatorname{U}_infty(C^ast_u(|mathbb{Z}^n|))$ is a homotopy equivalence. Moreover, when $n=1,2$, we determine the homotopy type of $operatorname{U}_1(C^ast_u(|mathbb{Z}^n|))$, which is the product of the unitary group $operatorname{U}_1(C^ast(|mathbb{Z}^n|))$ (having the homotopy type of $operatorname{U}_infty(mathbb{C})$ or $mathbb{Z}times Boperatorname{U}_infty(mathbb{C})$ depending on the parity of $n$) of the Roe algebra $C^ast(|mathbb{Z}^n|)$ and rational Eilenberg--MacLane spaces.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
