Bottomless Trap Hole can be used against a Synchro Summoned monster with appropriate attack, but it's not accurate to say it 'stops' the summon. In game terms, the summon is completed successfully, and cards like Bottomless Trap Hole will be used in response to that successful summon. It means though that Synchro Monsters like Brionac may have already used their effects due to player Priority - if you want to avoid even that happening, you need to negate the summon instead, with a summon negation card.
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A Fusion Summon, or the Summoning of any Monster (Synchro or Fusion) from the Fusion Deck (Extra Deck) is a special summon and so Trap Hole will not work on it.
Normal summon, no. Special summon, yes.The reason is, when Obelisk is normal summoned, no spells, traps or monster effects can be activated. That means it prevents anything being activated in the 'summon response' window, which is where you'd normally use cards like Trap Hole, Bottomless Trap Hole, Torrential Tribute, etc.
The current game-legal text for Slifer the Sky Dragon says "When Normal Summoned, cards or effects cannot be activated" This prevents the activation of Bottomless Trap Hole in response to Slifer's Normal summon. However this is only for Normal Summon. Slifer can be Special Summoned, and if Special Summoned, then his continuous effect will apply as normal, before cards that respond to summons can be activated. That means if he is special summoned, and his ATK goes to 2000, the summon can be responded to by Bottomless Trap Hole, he will be destroyed and removed.
Bottomless Trap Hole does not target, so Tyrant Dragon is unable to negate it.
The Calculator has a continuous effect that boosts its ATK. This effect becomes active the moment it is considered successfully summoned to the field. So, Player A places The Calculator on the field. He, or his opponent, have a chance to Counter the summon. If neither player counters it, the summon is successful. The Calculator's ATK changes to a new value. Now players can activate cards in response to the summon, this is where cards like Trap Hole or Torrential Tribute can be used. Bottomless Trap Hole can be used here also, and if The Calculator's new ATK is 1500 or over, it will be destroyed and removed.