Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
differential operators
|
| gptkbp:has_applications_in |
gptkb:topology
gptkb:Physics geometry mathematical physics |
| gptkbp:has_implications_for |
algebraic geometry
representation theory mathematical logic |
| https://www.w3.org/2000/01/rdf-schema#label |
Atiyah-Singer index formula
|
| gptkbp:is_analyzed_in |
manifolds
topological spaces |
| gptkbp:is_cited_in |
many mathematical texts
|
| gptkbp:is_connected_to |
index of Dirac operator
index of Laplace operator index of elliptic differential operators |
| gptkbp:is_considered |
a major achievement in mathematics
a cornerstone of modern mathematics |
| gptkbp:is_discussed_in |
numerous mathematical papers
|
| gptkbp:is_evaluated_by |
index of elliptic operators
|
| gptkbp:is_explored_in |
graduate studies
postgraduate research |
| gptkbp:is_expressed_in |
topological invariants
analytic invariants |
| gptkbp:is_fundamental_to |
modern mathematics
understanding of geometry understanding of differential equations understanding of topology |
| gptkbp:is_influential_in |
mathematical research
|
| gptkbp:is_part_of |
differential geometry
mathematical analysis global analysis theoretical frameworks in mathematics |
| gptkbp:is_related_to |
functional analysis
K-theory spectral theory characteristic classes heat equation |
| gptkbp:is_standardized_by |
Riemann-Roch theorem
|
| gptkbp:is_taught_in |
advanced mathematics courses
|
| gptkbp:is_used_in |
gptkb:quantum_field_theory
gptkb:string_theory mathematical physics research |
| gptkbp:named_after |
gptkb:Michael_Atiyah
gptkb:Isadore_Singer |
| gptkbp:proposed_by |
gptkb:Michael_Atiyah
gptkb:Isadore_Singer |
| gptkbp:provides |
relationship between geometry and analysis
|
| gptkbp:related_to |
index theory
|
| gptkbp:was_proven_in |
gptkb:1963
|
| gptkbp:bfsParent |
gptkb:Atiyah-Singer_Index_Theorem
|
| gptkbp:bfsLayer |
5
|