Remark on symplectic relative Gromov-Witten invariants and degeneration formula

TL;DR

This paper defends the validity of the degeneration formula for symplectic relative Gromov-Witten invariants by clarifying main ideas and responding to criticisms, asserting that the proof in [LR] is complete.

Contribution

It provides a detailed response to criticisms of [LR], affirming that the original proof of the degeneration formula is complete and clarifying the main ideas involved.

Findings

Confirmed the completeness of the proof in [LR]

Clarified main ideas behind the degeneration formula

Responded to misunderstandings in criticisms

Abstract

In this note, we give item-by-item responses to the criticisms raised in [TZ] by Tehrani ad Zinger on our paper [LR]. We illuminate the main ideas and contributions in [LR] in section 2, itemize the responses to issues raised in [TZ] and conclude that we have provided a complete proof of the degeneration formula in our published paper [LR] and its more detailed versions in arXiv. In [TZ], the authors made an effort in comparing the methods and ideas in [LR] vs [IP-1] [IP-2], but their criticisms on [LR] are based on their own lack of sufficient understanding of [LR].