Correct spelling for the English word "cobordant" is [kˈɒbɔːdənt], [kˈɒbɔːdənt], [k_ˈɒ_b_ɔː_d_ə_n_t] (IPA phonetic alphabet).
Cobordant is an adjective that describes a state of geometric or topological relationship between two objects or spaces. It refers to the condition where two objects or spaces share a common boundary or edge, making them adjacent or connected to each other.
In mathematics, cobordant is commonly used in the field of algebraic topology and differential geometry. In algebraic topology, cobordant refers to the relation between two manifolds or spaces that can be arranged with a common boundary. This means that given two manifolds, if their boundaries are topologically equivalent or can be deformed into each other, they are said to be cobordant. This concept is useful in studying the connectivity and relationship between different spaces or surfaces.
In differential geometry, cobordant refers to the relationship between two manifolds that can be smoothly joined together along a common boundary. This concept helps analyze the smoothness and compatibility of different geometric objects.
Overall, cobordant is a term used in mathematics to describe the connection or relationship between two objects or spaces that share a common boundary. It serves as a fundamental concept in understanding the topological or geometric properties and relationships in various branches of mathematics.