The fundamental group of the harmonic archipelago
Paul Fabel
Abstract
The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify the fundamental group pi1(HA) as a quotient of the Hawaiian earring group, provide a precise description of the kernel, show that both pi1(HA) and the kernel are uncountable, and that pi1(HA) has the indiscrete topology.
Create a lesson
Related papers
The p-local topologoical period-index problem in dimensions 2p+2 and below
Diarmuid Crowley, Xing Gu
Toward Quillen stratification for the odd primary Steenrod algebra
John H. Palmieri
Indecomposable Uniform Families on the Adams 4-Line
Jordan Benson, Runji Li
Sn-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products
Mohammadali Aligholi
Cohomology of regular spherical actions
José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak
Unfolding of symmetric monoidal (∞,n)-categories
Rune Haugseng, Thomas Nikolaus