query: Holes and generators of homology groups
positive_passages.docid: 91956
positive_passages.text: Intuition of the meaning of homology groups
negative_passages.docid: 3327
negative_passages.text: Height and minimal number of generators of an ideal
negative_passages.docid: 32172
negative_passages.text: Homomorphisms of graded modules
negative_passages.docid: 4790
negative_passages.text: Generators of a finitely generated free module over a commutative ring
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 148369
negative_passages.text: Quotient groups of D10
negative_passages.docid: 99689
negative_passages.text: Zeroth homotopy group: what exactly is it?
negative_passages.docid: 95031
negative_passages.text: Find generators of the ideal of an algebraic set
negative_passages.docid: 64021
negative_passages.text: Fundamental group of a torus with points removed
negative_passages.docid: 134032
negative_passages.text: Skew symmetry of indices in cocycles of Cech cohomology
negative_passages.docid: 112607
negative_passages.text: Why is homology invariant under deformation retraction/homotopy equivalence?
negative_passages.docid: 94018
negative_passages.text: Homology groups of $\mathbb{R}^3\setminus \ S^1$ and $\mathbb{R}^3\setminus E^1_+$
negative_passages.docid: 74305
negative_passages.text: Homology of a simplicial set
negative_passages.docid: 140612
negative_passages.text: Two homologous but not homotopic loops on a closed surface of genus greater than one
negative_passages.docid: 44258
negative_passages.text: Conditions under which group solvability is invariant under an homomorphism.
negative_passages.docid: 129452
negative_passages.text: Groups $G,H$ with surjective homomorphisms that are quotient of each other
negative_passages.docid: 23156
negative_passages.text: Homotopy equivalence from torus minus a point to a figure-eight.