BORDISM Meaning and
Definition
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Bordism is a concept in differential topology and algebraic topology that provides a mathematical framework for studying manifolds and their boundaries. It refers to the study of when two manifolds share the same boundary.
More formally, a bordism between two manifolds is a higher-dimensional manifold that has those given manifolds as its boundary. In other words, it captures the relationship between manifolds with the same boundary conditions.
Bordism theory seeks to understand and classify these bordisms by constructing mathematical invariants, known as bordism groups. These groups encode the essential topological information of the manifolds involved and provide a way to differentiate and classify them up to certain equivalence relations.
The concept of bordism has applications in various branches of mathematics, including differential geometry, algebraic geometry, and mathematical physics. It allows mathematicians to address questions related to the existence and structure of manifolds and to explore their interconnections.
Bordism also plays a fundamental role in the context of cobordism, which further generalizes the concept by considering manifolds equipped with additional structures, such as vector bundles. Cobordism theory provides a powerful tool for investigating the relationships between different geometric structures and has implications in fields like surgery theory and mathematical physics.
Overall, bordism is a crucial concept that helps mathematicians classify manifolds and study their boundary conditions within the realm of topology.
Common Misspellings for BORDISM
- vordism
- nordism
- hordism
- gordism
- birdism
- bkrdism
- blrdism
- bprdism
- b0rdism
- b9rdism
- boedism
- boddism
- bofdism
- botdism
- bo5dism
- bo4dism
- borsism
- borxism
- borcism
- borfism
Etymology of BORDISM
The term "bordism" was coined in mathematics and originates from the combination of two words: "border" and "ism". The "border" part of the word refers to the concept of a manifold's boundary. In mathematics, a manifold is a topological space that locally resembles Euclidean space, and its boundary is the set of points that are "on the edge" of the manifold.The suffix "-ism" is a commonly used linguistic element denoting a system or theory. It is often used to indicate a belief, action, or practice associated with a particular concept.When combined, "border" and "-ism" form "bordism", which is a theory in algebraic topology that studies the properties of manifolds based on their boundaries. Specifically, bordism theory focuses on defining and classifying manifolds up to the equivalence relation of having the same boundary by considering the cobordism relation between them.
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