homological invariant

C27157

concept

A homological invariant is a quantity or structure derived from homology theory that remains unchanged under specified transformations, used to distinguish and classify mathematical objects up to an appropriate notion of equivalence.

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All labels observed (8)

Label	Occurrences
cohomology class	6
algebraic K-theory	2
homological invariant canonical	2
categorified knot invariant	1
characteristic classes	1
multiplicative genus	1
smooth 4-manifold invariant	1
topological invariant relation	1

Description generation (CDg)

The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.

Instruction

generate a one-sentence description for a given conceptual class.
# Response Format
Return only the sentence: "Description: [one-sentence description of the conceptional class]"

Input

Class: homological invariant

Generated description

A homological invariant is a quantity or structure derived from homology theory that remains unchanged under specified transformations, used to distinguish and classify mathematical objects up to an appropriate notion of equivalence.

Instances (14)

Instance	Via concept surface
Castelnuovo–Mumford regularity	—
Chern classes	cohomology class
Milnor K-theory	algebraic K-theory
Todd class	cohomology class
Dolbeault cohomology classes surface form: Dolbeault cohomology class	cohomology class
Hirzebruch genera	multiplicative genus
Pontryagin classes	characteristic classes
Euler class	cohomology class
HOMFLY-PT homology	categorified knot invariant
Betti numbers	—
Stiefel–Whitney classes	cohomology class
Seiberg–Witten invariants	smooth 4-manifold invariant
Euler–Poincaré characteristic formula	topological invariant relation
Quillen K-theory	algebraic K-theory