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Homology-cohomology
New post in Homology-cohomology
The zeroth homology group corresponds to path components
August 1st, 2022
homology-cohomology
algebraic-topology
Difference between homology and integral homology?
August 1st, 2022
algebraic-topology
abstract-algebra
homology-cohomology
homological-algebra
Difference between cellular and simplicial homology
August 1st, 2022
homology-cohomology
algebraic-topology
De Rham cohomology of $\mathbb{R}^2 \setminus \{k~\text{points}\}$
August 1st, 2022
homology-cohomology
algebraic-topology
De Rham cohomology for non-compact manifolds
August 1st, 2022
differential-geometry
homology-cohomology
TDA - Persistence diagrams and Barcodes
August 1st, 2022
statistics
algebraic-topology
homology-cohomology
topological-data-analysis
The singular homology and cohomology of manifolds vanishes in high dimensions
August 1st, 2022
reference-request
homology-cohomology
manifolds
algebraic-topology
show that the compactly supported De Rham cohomology groups $H^{p}_{DR}(\mathbb{R^n})$ are all zero for $0\leq p<n$
August 1st, 2022
homology-cohomology
differential-topology
homology relative to homotopy equivalent subspaces
September 2nd, 2020
algebraic-topology
homology-cohomology
homotopy-theory
Homology groups of the Mapping Torus
November 20th, 2020
homology-cohomology
algebraic-topology
Question about the Betti numbers
August 1st, 2022
homological-algebra
betti-numbers
algebraic-topology
homology-cohomology
First homology group of a double torus (genus 2 surface) – intuition
August 1st, 2022
algebraic-topology
intuition
homology-cohomology
Moore Spaces: explicit CW-complex for $M(\mathbb{Z}_m, n)$
December 8th, 2020
homotopy-theory
algebraic-topology
homology-cohomology
cw-complexes
Removing a single point alters homology
August 1st, 2022
algebraic-topology
homology-cohomology
first Chern class of E is first Chern class of det E
July 5th, 2020
differential-geometry
homology-cohomology
The relative homology group $H_{1}(\mathbb{R},\mathbb{Q})$
August 1st, 2022
algebraic-topology
homology-cohomology
Non-orientable one dimensional manifold.
August 1st, 2022
homology-cohomology
algebraic-topology
About sheaf cohomology in algebraic geometry
August 1st, 2022
homology-cohomology
algebraic-geometry
Computing homology groups over different fields
August 1st, 2022
algebraic-topology
homology-cohomology
Homology of a simplicial set
April 20th, 2020
simplicial-stuff
homology-cohomology
algebraic-topology
Cech cohomology of $\mathbb A^2_k\setminus\{0\}$
August 1st, 2022
homology-cohomology
algebraic-geometry
sheaf-theory
Relative homology $H_n(T^2,S^1)$ (Hatcher, Exc 2.1,17.b)
August 23rd, 2020
algebraic-topology
proof-verification
homology-cohomology
exact-sequence
Prerequisites to study cohomology?
August 1st, 2022
homology-cohomology
group-cohomology
Constructing a surjective map $S^{n} \rightarrow S^{n}$ of degree zero
October 17th, 2020
algebraic-topology
homology-cohomology
De Rham cohomology of $\mathbb{R}^2 \setminus \{\text{one point}\}$
August 1st, 2022
algebraic-topology
smooth-manifolds
homology-cohomology
exact sequence of reduced homology groups
August 1st, 2022
algebraic-topology
homology-cohomology
$f_*$ induces an isomorphism in homology iff the mapping cone of $f_*$ is contractible.
August 1st, 2022
homology-cohomology
homological-algebra
Understanding the cartesian product of complex projective lines.
October 22nd, 2020
homology-cohomology
algebraic-topology
general-topology
cohomology vs homology
October 20th, 2020
homology-cohomology
homological-algebra
Top homology of a manifold with boundary
December 24th, 2020
homology-cohomology
algebraic-topology
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