Singular chains and the fundamental group
نویسندگان
چکیده
We show that the natural algebraic structure of singular chains on a path-connected topological space determines isomorphism class fundamental group functorially. Moreover, we describe notion weak equivalence for relevant
منابع مشابه
The Fundamental Group
The focus of this exposition is the fundamental group of a topological space. The paper begins by defining paths and homotopy, and proceeds to construct the fundamental group. Later, attention turns to the consequences of the construction, in particular to the fundamental group of S1 and Van Kampen’s Theorem.
متن کاملThe Fundamental Group
This is the next article in a series devoted to the homotopy theory (following [11] and [12]). The concept of fundamental groups of pointed topological spaces has been introduced. Isomorphism of fundamental groups defined with respect to different points belonging to the same component has been stated. Triviality of fundamental group(s) of R n has been shown. the terminology and notation for th...
متن کاملThe fundamental group and the first cohomology group
By a finite group cover of G, we will mean an M -definable connected group H with a surjective M -definable map H → G, whose kernel K is finite. The kernel K must lie within the center of H, because the action of H on K by conjugation yields a necessarily-trivial homomorphism from the connected group H to the finite group of automorphisms of K. If πi : Hi → G are finite group covers of G for i ...
متن کاملMonoids in the fundamental group . . .
We study monoids generated by Zariski-van Kampen generators in the 17 fundamental groups of the complement of logarithmic free divisors in C listed by Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them are free abelian monoids. The remaining four monoids are not Gaußian and, hence, are neither Garside nor Artin (Theorem 2). However, we introduce, similarly to Artin monoids,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2021
ISSN: ['0016-2736', '1730-6329']
DOI: https://doi.org/10.4064/fm734-6-2020