اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the failure of the first v{C}ech homotopy group to register geometrically relevant fundamental group elements
111
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We construct a space $mathbb{P}$ for which the canonical homomorphism $pi_1(mathbb{P},p) rightarrow check{pi}_1(mathbb{P},p)$ from the fundamental group to the first v{C}ech homotopy group is not injective, although it has all of the following properties: (1) $mathbb{P}setminus{p}$ is a 2-manifold with connected non-compact boundary; (2) $mathbb{P}$ is connected and locally path connected; (3) $mathbb{P}$ is strongly homotopically Hausdorff; (4) $mathbb{P}$ is homotopically path Hausdorff; (5) $mathbb{P}$ is 1-UV$_0$; (6) $mathbb{P}$ admits a simply connected generalized covering space with monodromies between fibers that have discrete graphs; (7) $pi_1(mathbb{P},p)$ naturally injects into the inverse limit of finitely generated free monoids otherwise associated with the Hawaiian Earring; (8) $pi_1(mathbb{P},p)$ is locally free.
قيم البحث
اقرأ أيضاً
Let $M$ be a topological monoid with homotopy group completion $Omega BM$. Under a strong homotopy commutativity hypothesis on $M$, we show that $pi_k (Omega BM)$ is the quotient of the monoid of free homotopy classes $[S^k, M]$ by its submonoid of n
ullhomotopic maps. We give two applications. First, this result gives a concrete description of the Lawson homology of a complex projective variety in terms of point-wise addition of spherical families of effective algebraic cycles. Second, we apply this result to monoids built from the unitary, or general linear, representation spaces of discrete groups, leading to results about lifting continuous families of characters to continuous families of representations.
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to the usual fundamental group as a special case. We also study weight
Unlike Grothendiecks etale fundamental group, Noris fundamental group does not fulfill the homotopy exact sequence in general. We give necessary and sufficient conditions which force exactness of the sequence.
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish homotopica
l purity and blow-up theorems for finite abelian groups.
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
