ﻻ يوجد ملخص باللغة العربية
Let $p$ be a prime. We calculate the connective unitary K-theory of the smash product of two copies of the classifying space for the cyclic group of order $p$, using a K{u}nneth formula short exact sequence. As a corollary, using the Bott exact sequence and the mod $2$ Hurewicz homomorphism we calculate the connective orthogonal K-theory of the smash product of two copies of the classifying space for the cyclic group of order two.
Let $k$ be an algebraically closed field, $l eqoperatorname{char} k$ a prime number, and $X$ a quasi-projective scheme over $k$. We show that the etale homotopy type of the $d$th symmetric power of $X$ is $mathbb Z/l$-homologically equivalent to the
The main result of this note is a parametrized version of the Borsuk-Ulam theorem. We show that for a continuous family of Borsuk-Ulam situations, parameterized by points of a compact manifold W, its solution set also depends continuously on the para
The topological Tverberg theorem states that given any continuous map $fcolonDelta^{(d+1)(r-1)}tomathbb{R}^d$, there are pairwise disjoint faces $sigma_1,ldots,sigma_r$ of $Delta^{(d+1)(r-1)}$ such that $f(sigma_1)capcdotscap f(sigma_r) eemptyset$ wh
In this note we prove the analogue of the Atiyah-Segal completion theorem for equivariant twisted K-theory in the setting of an arbitrary compact Lie group G and an arbitrary twisting of the usually considered type. The theorem generalizes a result b
In this paper we explain how Morse theory for the Yang-Mills functional can be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem. Classically, the Atiyah-Segal theorem relates the representation ring R(Gamma) of a compact Lie