とも無(な)く

ともなく and ともなしに are structures used to indicate that (A) was being done absentmindedly when (B) happened. It will be translated as 'unconsciously (A) when (B)', or 'without paying attention to (A), (B)'.
This pattern is a combination of the case-marking particle と, the adverbial particle も, and the conjunctive form of the い-Adjective ない. It will be seen after the dictionary form of verbs, and can be thought of as literally meaning something similar to 'even while not intending to (B), while (A), (B)'.

• 昨日(きのう)テレビを見(み)るともなく見(み)ていたら、急(きゅう)にお母(かあ)さんが出(で)てきたから驚(おどろ)いた。
  When I was absentmindedly watching TV yesterday, I was surprised when my mother suddenly appeared.
• 話(はなし)を聞(き)くともなく、先生(せんせい)と黒板(こくばん)の方向(ほうこう)をぼーっと見(み)ていた。
  I listened absentmindedly while staring towards the direction of my teacher and the blackboard.

ともなしに is similar, but pairs the noun なし 'without' with に, instead of using the conjugative form of ない.

• 飲(の)み会(かい)で上司(じょうし)の話(はなし)を聞(き)くともなしに聞(き)いていたら、「お前(まえ)はどう思(おも)う」と聞(き)かれたから適当(てきとう)に返事(へんじ)した。
  When I was at a drinking party and was absentmindedly listening to my boss, he asked what I thought, so I gave him a random response.
• 暇(ひま)だったから近所(きんじょ)を歩(ある)くともなしに歩(ある)いていたら、高校(こうこう)の同級生(どうきゅうせい)にばったりあった。
  When I was mindlessly walking in my neighborhood because I had nothing to do, I met my classmate from high school.

ともなく and ともなしに will often be seen in sentences that use たら. This puts emphasis on the specific time that something happened while performing another action absentmindedly. Despite translating this way, the action that precedes ともなく itself will be intentional, but the thing that comes about as a result of performing that action will not be what the doer was aiming to achieve.