In a filing with the U.S. Securities and Exchange Commission, Icahn said he, along with his affiliates, intend to discuss the possibility of board representation and ways to improve shareholder value with Hologic's management.
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Hologic's rights can be exercised if a person or group acquires 10 percent or more of the company's common stock.
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The company, which makes cancer screening tests, has been struggling with cuts in hospital spending and lack of reimbursement for one of its mammography system.
Hologic shares were up 7 percent at $23.85 in pre-market trading.