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Help resolving this contradiction in descriptions of the fundamental groups of the figure eight and n-torus

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#general-topology #algebraic-topology #fundamental-groups #free-groups #free-abelian-group
77
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$f$ has square root if and only if image of $f_*$ contained in $2 \mathbb Z$

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#algebraic-topology #connectedness #fundamental-groups
68
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Homotopic maps between pointed sets induce same group homomorphism

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#proof-verification #homotopy-theory #fundamental-groups
51
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If $H \le \pi_1(X,x)$ is conjugate to $P_*(\pi_1(Y, y))$, then $H \cong P_*(\pi_1(Y, y'))$ for some $y' \in P^{-1}(x)$

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#algebraic-topology #covering-spaces #fundamental-groups
424
Views

Calculating the fundamental group of $S^1$ with SvK

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#algebraic-topology #fundamental-groups
1.6k
Views

Monodromy representation.

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#ordinary-differential-equations #algebraic-topology #galois-theory #fundamental-groups
55
Views

A set of generators of $\pi_1(X,x_0)$ where $X=U\cup V$ and $U\cap V$ path connected

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#general-topology #fundamental-groups
93
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Is the fundamental group of the image a subgroup of the fundamental group of the domain?

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#algebraic-topology #examples-counterexamples #fundamental-groups
144
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Showing that $\pi_1(X/G) \cong G$.

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#topological-groups #fundamental-groups
411
Views

Fundamental group of a mapping cone

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#algebraic-topology #homotopy-theory #fundamental-groups
861
Views

Is there a subset of $\mathbb R^2$ that has fundamental group $\mathbb Z^2$?

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#algebraic-topology #fundamental-groups
1.3k
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Representation of fundamental group and flat bundle

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#representation-theory #vector-bundles #fundamental-groups #connections
241
Views

Manifolds covered by finitely many charts

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#algebraic-topology #manifolds #fundamental-groups
77
Views

Show that for an abelian countable group $G$ there exists a compact path connected subspace $K ⊆ \Bbb R^4$ such that $H_1(K)$ isomorphic to $G$

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#compactness #homology-cohomology #fundamental-groups #path-connected
907
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Show that the fundamental group of wedge of two circles is non Abelian without actually computing it.

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#algebraic-topology #homotopy-theory #fundamental-groups

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