Exhibit 4.1

FIRST SUPPLEMENTAL INDENTURE

Dated as of June 10, 2020

Between

COGENT COMMUNICATIONS GROUP, INC.

and

WILMINGTON TRUST, NATIONAL ASSOCIATION,

as Trustee

4.375% SENIOR NOTES DUE 2024

FIRST SUPPLEMENTAL INDENTURE, dated as of June 10, 2020 (this “Supplemental Indenture”), between COGENT COMMUNICATIONS GROUP, INC. (as successor by merger to Cogent Communications Finance, Inc.) (the “Company”), as issuer, and WILMINGTON TRUST, NATIONAL ASSOCIATION, as trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H:

WHEREAS, Cogent Communications Finance, Inc. (the “Escrow Issuer”), the Trustee, Deutsche Bank AG, London Branch, as paying agent, and Deutsche Bank Trust Company Americas, as registrar and authentication agent, are party to an Indenture, dated as of June 3, 2020 (together with any supplements thereto, the “Indenture”), providing for the issuance of the Escrow Issuer’s 4.375% Senior Notes due 2024 (the “Notes”);

WHEREAS, the Company is executing this Supplemental Indenture pursuant to which the Company shall become a party to the Indenture and assume all of the rights and be subject to all of the obligations and agreements of the “Company” under the Indenture;

WHEREAS, in connection with such assumption, the Company has duly authorized the execution and delivery of this Supplemental Indenture; and

WHEREAS, pursuant to Sections 9.01 and 9.05 of the Indenture, the Trustee is authorized to execute and deliver this Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company and the Trustee mutually covenant and agree for the benefit of the Holders of the Notes as follows:

1.       Capitalized Terms. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2.       Agreement to be Bound. Without limiting the assumption by operation of law upon the merger of the Escrow Issuer with and into the Company (with the Company surviving such merger), the Company hereby becomes party to the Indenture as the “Company” for all purposes thereof and as such will have all of the rights and be subject to all of the obligations and agreements of the “Company” under the Indenture.

3.       Ratification and Reaffirmation of Indenture; Supplemental Indenture Part of Indenture. Except as expressly amended hereby, the Indenture is in all respects ratified and reaffirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder of Notes heretofore or hereafter authenticated and delivered shall be bound hereby. The Trustee does not make any representation or warranty as to the validity or sufficiency of this Supplemental Indenture or as to the accuracy of the recitals to this Supplemental Indenture.

4.       No Recourse Against Others. No director, officer, employee, incorporator, stockholder, member, manager or partner of the Company, any Subsidiary or any direct or indirect parent of the Company, as such, will have any liability for any obligations of the Company under the Notes, the Indenture or this Supplemental Indenture or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder of Notes by accepting a Note waives and releases all such liability. The waiver and release are part of the consideration for issuance of the Notes. The waiver may not be effective to waive liabilities under the federal securities laws and it is the view of the SEC that such a waiver is against public policy.

5.       GOVERNING LAW. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

6.       WAIVER OF JURY TRIAL. EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS SUPPLEMENTAL INDENTURE OR THE TRANSACTIONS CONTEMPLATED HEREBY.

7.       Counterparts. The parties hereto may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. Delivery of an executed counterpart of a signature page to this Supplemental Indenture by facsimile, email or other electronic means shall be effective as delivery of a manually executed counterpart of this Supplemental Indenture.

8.       Headings. The section headings herein are for convenience only and shall not affect the construction hereof.

[Signature Pages Follow]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first written above.

[Cogent - Signature Page to Supplemental Indenture]

[Cogent - Signature Page to Supplemental Indenture]