query: General Linear Group is a manifold
positive_passages.docid: 21198
positive_passages.text: Proving that the general linear group is a differentiable manifold
negative_passages.docid: 145000
negative_passages.text: Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this?
negative_passages.docid: 146028
negative_passages.text: $GL(n, \mathbb{C})$ is isomorphic to a subgroup of $GL(2n, \mathbb{R})$
negative_passages.docid: 86572
negative_passages.text: Transverse Manifolds. Intersection is a Manifold again.
negative_passages.docid: 151637
negative_passages.text: How do we prove that this set is not manifold?
negative_passages.docid: 89649
negative_passages.text: Linear Algebra munkres analysis on manifolds question.
negative_passages.docid: 61616
negative_passages.text: category of linear maps
negative_passages.docid: 157742
negative_passages.text: Prove that $U(n)$ is a manifold
negative_passages.docid: 133413
negative_passages.text: Proof of paracompactness of CW-complexes (J. Lee, Introduction to Topological Manifolds)
negative_passages.docid: 90365
negative_passages.text: Riemannian Manifolds with $n(n+1)/2$ dimensional symmetry group
negative_passages.docid: 63098
negative_passages.text: Properly discontinuous actions and discrete groups in complete Riemannian manifolds.
negative_passages.docid: 72548
negative_passages.text: Lie group embeddings $SO(10) \supset SU(3) \times SU(2) \times U(1)?$
negative_passages.docid: 90092
negative_passages.text: Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
negative_passages.docid: 49666
negative_passages.text: Generalization of index 2 subgroups are normal
negative_passages.docid: 126930
negative_passages.text: Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
negative_passages.docid: 135126
negative_passages.text: Proving that the quotient manifold is orientable if and only if the group action is orientation-preserving
negative_passages.docid: 30794
negative_passages.text: Commutator Group of $GL_2(R)$ is $SL_2(R)$