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Lecture
Cellular Homology
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Related lectures (32)
Homology of Riemann Surfaces
Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
EML Spaces and Cohomology
Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.
Homology and Homotopy
Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Cohomology Groups: Hopf Formula
Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.
Topology Seminar: Tower Sequences and Homomorphisms
Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
Shape of Data: Algebraic Topology and Shape Representation
Covers algebraic topology, Betti numbers, and shape representation methods for efficient data shape measurement and analysis.
Singular Homology: First Properties
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Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.
Homology Groups: Basics
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Introduces reduced homology groups and explains their properties and applications in topology.
Simplicial and Singular Homology Equivalence
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Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.
Simplicial Homology Revisited
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Covers the concept of simplicial homology, focusing on finite complexes and induced maps.
Homology: Introduction and Applications
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Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.
Homology with coefficients
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Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
Cellular Homology: Applications
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Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.
Homology and the fundamental group
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Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.
Homotopy Invariance: Homology Groups
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Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.
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