Cleave is a verb with two very distinct definitions. In one sense it can mean to break two things apart, split one item into two pieces, or push something apart with great force. On the other hand, to cleave is to stick with something very closely, like a belief or a person.
These two opposing definitions also have differing verb forms. To adhere to something in the past tense is to cleaved, clove, and clave, though the latter two are rare and slightly archaic. To break something into two in the past tense is to cleaved and clove, but also to have cleaved, have cleft, or have cloven.
Cleavage is the act of separating or a state of being split apart. By far, its most common reference is to how much of a woman’s breasts are showing from her clothing.
Side note: It seems as if cleave is also gaining a small bit of ground as a shortened version of cleavage, though this use is colloquial at best.
Examples
To break apart
So why did eBay put up so much resistance to Icahn’s proposal to cleave the company in two? [SF Gate]
The interventions of the banks and supermarkets, warning of head offices moved to London and hikes in shopping basket prices, will have shifted undecideds to No and even cleaved some soft Yeses away. [STV News]
Now he sported a great iron plate where my sword had so easily cleft into his skull. [The Telegraph]
“When I see the great principles of personal liberty and the rights of property being cloven down by the men now running the machine of Government, ‘the ancient landmarks’ of the Constitution ‘which our fathers set’ removed, I feel like crying, in the language of the Holy Writ, ‘cursed be he that removeth them.’” [The New York Times]
A ‘bra cam’ that records people checking out a woman’s cleavage is fast becoming a viral video hit – and all for a good cause. [Belfast Telegraph]
To cling to
Other requirements, of course, cleave to USDA regulations around things like calorie and fat content. [Seattle Weekly]
he notion that positive thinking is correlated with good health puts enormous pressure on people to cleave to beliefs that they don’t actually trust. [Slate]
But it is not simply those whom sociologists call “the left behind” who have cleaved to the independence camp in Scotland. [New York Times]