The king is pretty safe here.
1. d2d4  1... g8f6  2. c2c4  2... e7e6  3. b1c3  3... f8b4  4. g1f3  4... b4c3 A pretty straightforward approach, but relatively rare. Although, how can the doubling of the pawns can be a rare idea in the Nimzo-Indian $2 5. b2c3  5... d7d6 Building the pawns a'la Capablanca, on the color of the missing bishop, is the quintessence of the line. 6. d1c2  6... d8e7 [#] 7. a2a4 [%c_effect a4;square;a4;type;Interesting;persistent;true] A nice move by Fedoseev, and a novelty. 7... c7c5 [%c_effect c5;square;c5;type;GreatFind;persistent;true] Unlike Kramnik, Carlsen is very aware of the vulnerability of his dark squares and builds a rock-solid wall against the opponent's dark-squared bishop. 8. e2e4  8... e6e5 Building the so-called Portisch-Huebner wall. 9. d4d5 This is often a concession. The closing of the center typically works well for the second player. 9... b8d7 Here and on the next few moves Black could have locked the queenside. 10. h2h4 Fedoseev, too, had a few opportunities to seize a bit more space on the queenside. However, White believes that it is more important to discourage his opponent from kingside castling while gaining more space on that part of the board. 10... h7h6  11. f1e2  11... e8d8 Another typical maneuver for the line and a favorite of Karpov's. 12. f3d2 