Topology (noun, “top-AH-low-jee”)

Topology is a field of math that focuses on how molding or stretching a shape alters the space it takes up.

In a way, topology is similar to geometry. Both fields study shapes. However, geometry focuses on rigid measurements, such as the length of lines in a triangle. It answers questions like: If I change the length of this line, how will the other lines change? In geometry, the new triangle is considered a different triangle altogether.

But topology does not focus on such rigid measurements. Instead, topology treats the study of shapes like a game. As in a game, a topologist sets out certain rules. Then, they explore what shapes are possible within those rules.

For instance, a rule might be that all the shapes in a certain family can morph into one another without tearing or gluing parts together. You could explore this yourself by squeezing a water balloon. As you watch the balloon warp, you see continuous changes to its shape. Squeezing the middle causes the outsides to bulge. But the balloon doesn’t break or form new connections. So, all the shapes the balloon takes still obey the rule.

A mathematician might say that all the shapes of this balloon belong to the same topological group.

Another rule might be that all the shapes in a group must have one hole. A donut is an obvious member of this group. But so is a mug. If you made both of these shapes out of clay, you could remold one into the other without tearing the clay or attaching any new pieces. Under the one-hole rule, they are in the same topological family.

A particularly mind-twisty rule might be that all shapes in a family have “non-orientable surfaces.” That means the shape doesn’t have a clear outside and inside. A loop with a twist in it, called a Möbius strip, is a famous example.

Topology can be represented in many ways. Computer models can render and play with shapes. The math of algebra can describe concepts in topology, too.

Setting up rules for shapes and playing around with them is more useful than you might think. It helps scientists understand what is physically possible and impossible. Engineers can use these insights to imagine new technologies. Cosmologists use topology to describe the shape of our universe. And physicists who study string theory use it to probe the nature of matter.

In a sentence

A Möbius strip is one famous example of a curiously mind-bending shape from the field of topology.

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A small member of our solar system out beyond Pluto may be shrouded in a thin layer of gas. If so, it would be the first object of its size — and the most remote rock in our solar system — known to host even a wispy atmosphere.

“This discovery suggests that small icy worlds beyond Neptune may not be as inactive or unchanging as we often assumed,” says Ko Arimatsu. “Until now, Pluto was the only [object beyond Neptune] with a confirmed atmosphere.”

Arimatsu is an astronomer at the National Astronomical Observatory of Japan. It’s in Mitaka. His group shared the new finding May 4 in Nature Astronomy.

Arimatsu’s group tracked the object — known as 2002 XV₉₃ — with a network of telescopes in Japan. On January 10, 2024, those telescopes saw it move in front of a distant star. Such tiny eclipses are called occultations (Ah-kul-TAY-shuns). They can reveal whether some object in our solar system hosts an atmosphere.

If 2002 XV₉₃ were bare, the star behind it would have seemed to blink out and reappear sharply. But Arimatsu and his teammates saw the star’s light gradually fade and reappear over about 1.5 seconds. That smooth dimming is best explained by starlight passing through a layer of gas. Those data suggest this thin atmosphere has a pressure about one ten-millionth that of Earth’s.

“I was genuinely surprised,” Arimatsu says. The object is about 470 kilometers (290 miles) wide. The Grand Canyon is about that long. At such a small size, 2002 XV₉₃’s gravity should be too weak to hold on to a gas for long. So its atmosphere should have vanished long ago, unless something has added new gas to it.

Perhaps an icy body like a comet recently smashed into 2002 XV₉₃. That could have released a plume of gas around the object. Or maybe 2002 XV₉₃ releases gas regularly from icy volcanoes on its surface.

The astronomers can’t be certain what’s going on just from viewing 2002 XV₉₃ pass in front of one star. The data couldn’t show what the atmosphere is made of. So the small body might even be swaddled in dust, not gas, Arimatsu notes. Nor could they show how high above the body’s surface any atmosphere extends.

“Future observations will be important,” he says. Say its atmosphere fades over the next few years. That could mean he had detected a plume kicked up by an impact. If it sticks around or varies over time, that might make a case for surface volcanoes.