query: What are the homology groups $H_k(\mathbb{R}\setminus \{0\})$?
positive_passages.docid: 153092
positive_passages.text: Homology of disjoint union is direct sum of homologies
negative_passages.docid: 122410
negative_passages.text: Can one build a homology theory using submanifolds and their boundaries?
negative_passages.docid: 52548
negative_passages.text: Topological group: Multiplying two loops is homotopic to linking these paths?
negative_passages.docid: 2871
negative_passages.text: Spaces with equal homotopy groups but different homology groups?
negative_passages.docid: 18893
negative_passages.text: $\varphi:G\to H$ is a Lie Group Homomorphism, then $\ker \varphi$ has Lie algebra $\ker D_e \varphi$
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: 16860
negative_passages.text: set of almost complex structures on $\mathbb R^4$ as two disjoint spheres
negative_passages.docid: 78624
negative_passages.text: CW complexes and manifolds
negative_passages.docid: 101064
negative_passages.text: Showing the triviality of homomorphisms
negative_passages.docid: 89215
negative_passages.text: How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
negative_passages.docid: 74305
negative_passages.text: Homology of a simplicial set
negative_passages.docid: 57468
negative_passages.text: Continuous homorphisms between topological groups.
negative_passages.docid: 29269
negative_passages.text: fundamental group of $GL^{+}_n(\mathbb{R})$
negative_passages.docid: 84630
negative_passages.text: Homology of orientable surface of genus $g$
negative_passages.docid: 58135
negative_passages.text: Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
negative_passages.docid: 99689
negative_passages.text: Zeroth homotopy group: what exactly is it?
negative_passages.docid: 4462
negative_passages.text: Homotopy invariance for cohomology