The concept of continuous-time trajectory representation has brought increased accuracy and efficiency to multi-modal sensor fusion in modern SLAM. However, regardless of these advantages, its offline property caused by the requirement of global batch optimization is critically hindering its relevance for real-time and life-long applications. In this paper, we present a dense map-centric SLAM method based on a continuous-time trajectory to cope with this problem. The proposed system locally functions in a similar fashion to conventional Continuous-Time SLAM (CT-SLAM). However, it removes the need for global trajectory optimization by introducing map deformation. The computational complexity of the proposed approach for loop closure does not depend on the operation time, but only on the size of the space it explored before the loop closure. It is therefore more suitable for long term operation compared to the conventional CT-SLAM. Furthermore, the proposed method reduces uncertainty in the reconstructed dense map by using probabilistic surface element (surfel) fusion. We demonstrate that the proposed method produces globally consistent maps without global batch trajectory optimization, and effectively reduces LiDAR noise by surfel fusion.