I want to build a integrated application focusing on only one contract, the deployment and transactions sending, how can such an application communicate with the ethereum network without geth interface without mist? the RPC interface? any detailed documentations regarding this you recommend?
I think you wrote the answer in your question. I can't see any other mean that using RPC on a remote node. You can rewrite an API over the node RPC API if you want to restrict some usages and hide your node behind a firewall, but that remains the same process.
If you don't want to run a node (Geth), than your app will need to talk to "something" that can act as a proxy between your application and the Ethereum network.
A common approach to do this would be to run a web application that talks to a local Ethereum node over JSON RPC and can pass requests from your application to the Ethereum network (maybe over plain HTTP(S) or a websocket). Your application would need to sign and send raw transactions for any write operations to your contract. Of course, a potential problem with this is that you have now introduced a centralized component into your decentralized application.
Ideally over time, Ethereum node performance will improve to the point that it'll be acceptable to always run them with your application - as Mist is doing now; so decentralized applications can stay truly decentralized. This may not be that far away, both Geth and Parity have greatly improved in a very short amount of time.