Topology

34 Pins
·
3y
Every world in a grain of sand: John Nash’s astonishing geometry
Isometric embedding of the square flat torus in ambient space. Hevea Project, CC BY-SA Click to enlarge More pictures are available at the Project’s website.
Are there "principal" bundles $S^1 \to S^3 \to S^2$ other then Hopf's? (They would be necessarily not locally trivial)
at.algebraic topology - Are there "principal" bundles S^1 --> S^3 ---> S^2 other then Hopf's? (They would be necessarily not locally trivial) - MathOverflow
Nobel Prize Awarded for Quantum Topology | Quanta Magazine
Nobel Prize Awarded for Quantum Topology | Quanta Magazine More
Borromean Knot Mandala I Original Watercolor - Etsy
Borromean Knot Mandala I original watercolor by HelenKlebesadelArt, $900.00
Gallery : Knots and dynamics
Mathematical imagery by Jos Leys in collaboration with Prof. Etienne Ghys of the Ecole Normale Supérieure de Lyon. Gallery : Knots and dynamics
Why is it called a "Klein Bottle"?
Why is it called a "Klein Bottle"?
Group theory - Wikipedia
A torus. Its abelian group structure is induced from the map C → C/Z + τZ, where τ is a parameter living in the upper half plane.
Exotic spheres, or why 4-dimensional space is a crazy place
"Lovecraft had some interest in mathematics, and indeed used ideas such as hyperbolic geometry to lend extra strangeness to his stories... But he could not have known how fortunate was the decision to represent Yog-Sothoth in this manner. Strange spheres really are the keys to higher dimensional worlds, and our understanding of them has increased greatly in recent years.. a subject called differential topology has grown up, and revealed just how alien these places are."