boundary homomorphism
A crucial concept in algebraic topology, particularly in the study of homology and cohomology theories.
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Definition
C2Algebraic Topology
(technical, academic)A structure-preserving function that maps elements from a higher-dimensional chain group to a lower-dimensional one, often used to analyze the connectivity and structure of simplicial complexes.
Example
- In algebraic topology, the boundary homomorphism helps determine the boundaries of simplicial complexes.
- The boundary homomorphism is essential for defining homology groups.
C2Simplicial Chain Complex
(technical, academic)A function on the group of simplicial k-chains that maps each oriented k-simplex to a formal sum of its faces.
Example
- The boundary homomorphism of a k-simplex is calculated by summing its faces with alternating signs.
- Understanding the boundary homomorphism is key to studying the chain complex of a simplicial complex.
Similar
Terms that have similar or relatively close meanings to "boundary homomorphism":
connecting homomorphismboundary termboundary cornerboundary rider