Algebraic topology Definition and 59 Threads

Hi everyone! I would like to solve some questions: Classify up to isomorphism the four-sheeted normal coverings of a wedge of circles. describe them. i tried to to this and it is my understanding that such four sheeted normal coverings have four vertices and there are loops at each of...

I am trying to show that the space Cone(L(X,x)) is homeomorphic to P(X,x) where L(X,x) = {loops in X base point x} and P(X,x) = {paths in X base point x} I firstly considered (L(X,x) x I) and tried to find a surjective map to P(X,x) that would quotient out right but i couldn't seem to find...

Hey, can anyone help me with this please. I am doing algebraic topology and am particularly stuck on exact sequences. I "understand" the idea of the definition for example: 0\rightarrow A\stackrel{\alpha}{\rightarrow}B\stackrel{\beta}{\rightarrow}C\rightarrow 0 in this short exact...

I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.

Note: I have many questions and will keep posting new ones as they come up. To find the questions simply scroll down to look for bold segments. Feel free to contribute any other comments relevant to the questions or the topic itself. Here it is... Let p:E->B be continuous and surjective...

I'm totally stuck on these two. The first is... Let A be a subset of X; suppose r:X->A is a continuous map from X to A such that r(a)=a for each a e A. If a_0 e A, show that... r* : Pi_1(X,a_0) -> Pi_1(A,a_0) ...is surjective. Note: Pi_1 is the first homotopy group and r* is the...

Please read the following problem first: Suppose n > 1 and let S^n be the n-sphere in R^{n+1}. Let e be the unit-coordinate vector (1,0,...,0) on S^n. Prove that the fundamental group pi_1(S^n;e) is the trivial group. Okay, now my question is what does the notation "pi_1(S^n;e)" mean...

i know that geometric topology is a field that is connected to knot theory, i wonder what are the similarities between the two subjects, and in what subject in particular they overlap?

What are the main differences in approach between standard? topology and algebraic topology?