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                                                                     Exhibit 4.4


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                    ALLIED RISER COMMUNICATIONS CORPORATION,

                                     ISSUER,


                       COGENT COMMUNICATIONS GROUP, INC.,

                                   CO-OBLIGOR,


                                       AND


                            WILMINGTON TRUST COMPANY,

                                     TRUSTEE


                                   ----------



                          FIRST SUPPLEMENTAL INDENTURE

                          Dated as of January ___, 2002


                                       TO


                                    INDENTURE

                            Dated as of June 28, 2000


                                   ----------



                  7.50% CONVERTIBLE SUBORDINATED NOTES DUE 2007



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         FIRST SUPPLEMENTAL INDENTURE, ("First Supplemental Indenture") dated as
of January ___, 2002, among ALLIED RISER COMMUNICATIONS CORPORATION, a
corporation duly organized and existing under the laws of the State of Delaware,
having its principal office at 1700 Pacific Avenue, Suite 400, Dallas, Texas
75201 (herein called the "Company"), COGENT COMMUNICATIONS GROUP, INC., a
corporation duly organized and existing under the laws of the State of Delaware,
having its principal office at 1015 Thirty-First Street, N.W., Washington, D.C.
20007 (herein called "Cogent"), and WILMINGTON TRUST COMPANY, a banking
corporation, not in its individual capacity but solely as Trustee hereunder and
under the Indenture (as defined below) (herein called the "Trustee").
Capitalized terms not otherwise defined herein shall have the meanings set forth
in the Indenture.

                                    RECITALS

         WHEREAS, the Company and the Trustee have heretofore executed and
delivered a certain Indenture, dated as of June 28, 2000 (the "Indenture"),
providing for the issuance of Securities and, subject to and upon compliance
with applicable provisions of the Indenture, the conversion of any Security at
the option of the Holder thereof into fully paid and nonassessible shares of
Common Stock of the Company at the Conversion Rate in effect at the time of
conversion;

         WHEREAS the Company, Cogent and Augustus Caesar Merger Sub, Inc., a
corporation duly organized and existing under the laws of the State of Delaware
and a wholly owned subsidiary of Cogent (the "Merger Sub"), have entered into an
Agreement and Plan of Merger, dated as of August 28, 2001, as amended by
Amendment No. 1, dated as of October 13, 2001 (as so amended, the "Merger
Agreement"), which contemplates the execution and filing of a certificate of
merger (the "Certificate of Merger") providing for the merger of the Merger Sub
with and into the Company (the "Merger"), with the Company continuing its
corporate existence under the laws of the State of Delaware;

         WHEREAS, Section 7.1 of the Indenture provides, among other things,
that upon the merger of any other Person with or into the Company, the due and
punctual payment of the principal of, premium, if any, and interest on all of
the Securities as applicable, and the performance or observance of every
covenant of the Indenture to be performed or observed by the Company shall be
expressly assumed, by an indenture supplemental to the Indenture, executed and
delivered to the Trustee, in form satisfactory to the Trustee by the Person with
or into which the Company shall have been merged;

         WHEREAS, under the Merger Agreement and at the effective time of the
Merger, each share of common stock of the Company, par value $0.0001 per share,
will be converted into the right to receive 0.0321679 shares of common stock of
Cogent, par value $0.001 per share, and the Company shall become a wholly owned
subsidiary of Cogent;

         WHEREAS, Section 7.1 of the Indenture further provides, among other
things, that any Person into or with which the Company is merged shall have
provided for conversion rights in accordance with Article XII;

         WHEREAS, Section 8.1 of the Indenture provides, among other things,
that, without the


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consent of any Holders of Securities, the Company, when authorized by a Board
Resolution of the Company, and the Trustee, at any time and from time to time,
may enter into one or more indentures supplemental to the Indenture to evidence
the succession of another Person to the Company and the assumption by any such
successor of the covenants and obligations of the Company in the Indenture and
in the Securities;

         WHEREAS, the execution and delivery of this First Supplemental
Indenture has been authorized by resolutions of the board of directors of the
Company and by resolutions of the board of directors of Cogent;

         NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

         For and in consideration of the premises and intending to be legally
bound hereby, it is mutually covenanted and agreed, for the equal and
proportionate benefit of all Holders of the Securities, as follows:

                                    ARTICLE I
                    REPRESENTATIONS OF THE COMPANY AND COGENT

         Each of the Company and Cogent represents and warrants as of the date
hereof and as of the time the Merger becomes effective to the Trustee as
follows:

         SECTION 1.1. It is a corporation duly organized, validly existing and
in good standing under the laws of the State of Delaware.

         SECTION 1.2. The execution, delivery and performance by it of this
First Supplemental Indenture have been authorized and approved by all necessary
corporate action on its part.

                                   ARTICLE II
                   CONFIRMATION AND ASSUMPTION OF OBLIGATIONS

         SECTION 2.1. The Company hereby confirms its obligations in respect of
the due and punctual payment of the principal of, premium, if any, and interest
on all of the Securities as applicable, and the performance or observance of
every covenant of the Indenture to be performed or observed by the Company.

         SECTION 2.2. Cogent hereby assumes, as of the date hereof, pursuant to
this First Supplemental Indenture and as the co-obligor of the Company, all
obligations in respect of the due and punctual payment of the principal of,
premium, if any, and interest on all of the Securities as applicable, and the
performance or observance of every covenant of the Indenture to be performed or
observed by the Company.

         SECTION 2.3. The Holder of each Security that is Outstanding as of the
date hereof shall have the right, during the period such Security shall be
convertible as specified in Section 12.1 of the Indenture, to convert such
Security only into the kind and amount of common stock of Cogent receivable upon
the Merger by a holder of the number of shares of common stock of the Company
into which such Security might have been converted immediately prior to the
Merger, assuming such holder of common stock of the Company is not a Constituent
Person or


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an Affiliate of a Constituent Person. From and after the Effective Time, the
Conversion Rate shall be subject to adjustments from time to time which shall be
as nearly equivalent as may be practicable to the adjustments provided for in
Article XII of the Indenture.

         SECTION 2.4. Securities authenticated and delivered after the execution
of this First Supplemental Indenture may, and shall if required by the Trustee,
bear a notation in form approved by the Trustee as to any matter provided for in
this First Supplemental Indenture.

         SECTION 2.5. Upon the effective time of this First Supplemental
Indenture, Cogent may exercise every right and power of the Company under the
Indenture with the same effect as if Cogent had been named as a co-obligor of
the Company in the Indenture.

         SECTION 2.6. Pursuant to Section 14.5 of the Indenture, as of the date
hereof, the provisions of the Indenture relating to the right of Holders to
cause repurchase of the Securities following a Change in Control are hereby
modified to make such provisions in the Indenture apply, in the event of a
Change in Control subsequent to the effective time of this First Supplemental
Indenture, to the common stock of Cogent and to Cogent, as follows:

                  The first sentence of the definition of "Common Stock" in
         Section 1.1 of the Indenture is hereby modified and amended to read as
         follows:

                  "Common Stock" means the Common Stock, par value $0.001 per
         share, of Cogent Communications Group, Inc. authorized as of the
         effective date of the First Supplemental Indenture hereto.

                                   ARTICLE III
                                  MISCELLANEOUS

         SECTION 3.1. This First Supplemental Indenture constitutes an integral
part of the Indenture, which, as supplemented and amended by this First
Supplemental Indenture, is in all respects hereby adopted, ratified and
confirmed.

         SECTION 3.2. Notice of the execution of this First Supplemental
Indenture shall be given by the Company to the Holder of each Security as
provided in Sections 1.6 and 12.11 of the Indenture promptly upon such execution
hereof.

         SECTION 3.3. The recitals contained herein shall be taken as the
statements of the Company and Cogent, and the Trustee does not assume any
responsibility for their correctness. The Trustee makes no representations as to
the validity or sufficiency of this First Supplemental Indenture.

         SECTION 3.4. The Trustee acknowledges that the Company has delivered to
the Trustee, in accordance with Sections 7.1(3), 8.3 and 12.11 of the Indenture,
an Officers' Certificate and an Opinion of Counsel.

         SECTION 3.5. If any provision of this First Supplemental Indenture
limits, qualifies or conflicts with the duties imposed by any of Sections 310 to
317, inclusive, of the Trust Indenture Act through operation of Section 318(c)
thereof, such imposed duties shall control.


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         SECTION 3.6. Nothing in this First Supplemental Indenture, express or
implied, shall give to any Person, other than the parties hereto and their
successors and assigns, any benefit or any legal or equitable right, remedy or
claim under this First Supplemental Indenture.

         SECTION 3.7. This First Supplemental Indenture shall be governed by and
construed in accordance with the laws of the State of New York, and for all
purposes shall be governed by and construed in accordance with the laws of such
State, without regard to the conflicts of laws principles thereof.

         SECTION 3.8. This First Supplemental Indenture may be executed in any
number of counterparts, each of which so executed shall be deemed to be an
original, but all such counterparts shall together constitute but one and the
same instrument.

         SECTION 3.9. This First Supplemental Indenture shall become effective
as of 5:00 p.m. New York City time on the date hereof.

         IN WITNESS WHEREOF, the parties hereto have caused this First
Supplemental Indenture to be duly executed all as of the day and year first
above written.

                           ALLIED RISER COMMUNICATIONS CORPORATION


                           By:
                               -------------------------------------------------
                               Name:    [Gerald Dinsmore]
                               Title:   [Chief Executive Officer]



                           COGENT COMMUNICATIONS GROUP, INC.


                           By:
                               -------------------------------------------------
                               Name:    [David Schaeffer]
                               Title:   [Chairman and Chief Executive Officer]



                           WILMINGTON TRUST COMPANY,
                           not in its individual capacity but solely as Trustee
                           hereunder and under the Indenture


                           By:
                               -------------------------------------------------
                               Name:    [Michael W. Diaz]
                               Title:   [Authorized Signer]


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