On Holomorphic Contractibility of Teichmüller Spaces

Round 1

Reviewer 1 Report

The author gives a refined proof for the problem of holomorphic contractibility of Teichmüller spaces which he recently solved in [13]. Moreover, in the present paper he provides two independent proofs of holomorphic contractibility for low dimensional Teichmüller spaces. Since the results are already known, there is no need to doubt their correctness. Altogether, the new methods to prove the results are interesting and well motivated.

The paper is organised clearly and reasonably. In Section 1 the problem and its history are introduced and Section 2 contains discussion and results which establish a basis for Sections 3 and 4. In Section 3 the author proves the main result of the paper, this is, the holomorphic contractibility of all Teichmüller spaces T(0,n). In Section 4 he gives a second proof of holomorphic contractibility for low dimensional Teichmüller spaces.

In my opinion the paper is well written and it contains new mathematical ingredients. It is closely connected to the scientific work of Prof. A. A. Gol'dberg. Hence I strongly recommend the paper for publication in Axioms Honorary Special Issue Dedicated to his memory.

Author Response

I am very thankful to the referees for their remarks and suggestions. 

All these remarks and suggestions are accepted, and the corresponding corrections are installed in the text. 

In particular, the fact that all spaces T(0, n) are holomorphically contractible in view of its importance is now framed in the paper as Theorem 3. 

 

Reviewer 2 Report

The author needs to take into account some small remarks before publishing the paper. The remarks are in the file attached.

Comments for author File: Comments.pdf

Author Response

I am very thankful to the referees for their remarks and suggestions. 

All these remarks and suggestions are accepted, and the corresponding corrections are installed in the text.