English
... 2.3. CW-complexes. One of the difficulties for computing homotopy groups is that given two arbitrary topological spaces X and Y , it is difficult to construct any continuous map f : X → Y . In this section we will only try with a class of spaces built up step by step out of simple building blocks, a ...
... 2.3. CW-complexes. One of the difficulties for computing homotopy groups is that given two arbitrary topological spaces X and Y , it is difficult to construct any continuous map f : X → Y . In this section we will only try with a class of spaces built up step by step out of simple building blocks, a ...
connected spaces and how to use them
... connected, it makes sense to ask how many pieces it has. WARNING: the definition below ONLY deals with the situation when X has FINITELY MANY pieces (connected components). This is not always true - there spaces with infinitely many components (think Q, for example). However, in the infinite case a ...
... connected, it makes sense to ask how many pieces it has. WARNING: the definition below ONLY deals with the situation when X has FINITELY MANY pieces (connected components). This is not always true - there spaces with infinitely many components (think Q, for example). However, in the infinite case a ...
FINITE CONNECTED H-SPACES ARE CONTRACTIBLE Contents 1
... 4. Finite H-spaces This and the following two sections review work of Stong [5]. Definition 4.1. Let X be a topological space, e ∈ X a basepoint. Equip (X, e) with continuous product map φ : X × X → X. Write xy for φ(x, y). We now say (X, e) is an H-space if the maps θ1 : X → X : x 7→ xe and θ2 : X ...
... 4. Finite H-spaces This and the following two sections review work of Stong [5]. Definition 4.1. Let X be a topological space, e ∈ X a basepoint. Equip (X, e) with continuous product map φ : X × X → X. Write xy for φ(x, y). We now say (X, e) is an H-space if the maps θ1 : X → X : x 7→ xe and θ2 : X ...
RIGID RATIONAL HOMOTOPY THEORY AND
... Suppose that k is a finite field, and X{k is a geometrically connected variety (“ separated scheme of finite type). Question. Is there a way to ’do algebraic topology on X’ ? More specifically, we can ask if there are cohomology functors H i pXq which is some way behave like the singular cohomology ...
... Suppose that k is a finite field, and X{k is a geometrically connected variety (“ separated scheme of finite type). Question. Is there a way to ’do algebraic topology on X’ ? More specifically, we can ask if there are cohomology functors H i pXq which is some way behave like the singular cohomology ...
Global Calculus:Basic Motivations
... Let us begin with the category of sets. Suppose M is the topological space and S is a fixed set. Given any subset U of M (open or not), we can consider the set S U of functions from U to S. Define, now, a presheaf A as follows: • For every open set U , associate the set of functions from U to S. Tha ...
... Let us begin with the category of sets. Suppose M is the topological space and S is a fixed set. Given any subset U of M (open or not), we can consider the set S U of functions from U to S. Define, now, a presheaf A as follows: • For every open set U , associate the set of functions from U to S. Tha ...