query: Fundamental Group of $GL_r(\mathbb{C})$
positive_passages.docid: 145000
positive_passages.text: Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?
negative_passages.docid: 55493
negative_passages.text: Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
negative_passages.docid: 43004
negative_passages.text: Why are there $|G/G'|$ 1-dimensional representations of $G$?
negative_passages.docid: 141190
negative_passages.text: Fundamental group of mapping torus?
negative_passages.docid: 11000
negative_passages.text: Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$
negative_passages.docid: 30637
negative_passages.text: Exponent of $GL(n,q)$.
negative_passages.docid: 151699
negative_passages.text: Group of inner automorphisms of a group $G$
negative_passages.docid: 151210
negative_passages.text: How can we find and categorize the subgroups of $\mathbb{R}$?
negative_passages.docid: 90764
negative_passages.text: Prove that the fundamental group of the circle is non-trivial if the fundamental group of a space $X$ is non-trivial
negative_passages.docid: 87922
negative_passages.text: Computing the Lie bracket on the Lie group $GL(n, \mathbb{R})$
negative_passages.docid: 91085
negative_passages.text: how to find $|GL_2(F_p)|$
negative_passages.docid: 55070
negative_passages.text: Fundamental group of complement of $n$ lines through the origin in $\mathbb{R}^3$
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
negative_passages.docid: 58135
negative_passages.text: Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
negative_passages.docid: 102284
negative_passages.text: $GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$
negative_passages.docid: 21198
negative_passages.text: Proving that the general linear group is a differentiable manifold
negative_passages.docid: 105666
negative_passages.text: What's an easy way to show that $GL(n,\mathbb C)$ is connected?