Researched
Topology
Poincaré's Analysis Situs (1895) studies properties of shapes that survive stretching and bending, such as holes and connectedness.
Open in the interactive tree →Building on Euler, Riemann and Cantor's point sets, topology became a central field of mathematics; the Poincaré conjecture and homology are early landmarks. Its ideas now appear in physics (topological phases), data analysis and the Hodge conjecture.
Prerequisites
Unlocks
- Poincaré Conjecture Proved2003
- Hodge ConjectureopenThe Hodge conjecture links algebraic geometry to the topology of cohomology classes
- Algebraic Cycles UnderstoodopenAlgebraic cycles are studied through topological invariants