My brother and I own residential real estate that we are selling.How can the capital gains be deferred if on the new property purchased,my brother is not listed?

Is it a rental property?

Yes.  It is a townhouse that my parents originally purchased (my parents continued to live there after transferring title to my brother and me and paid monthly rent).

and did you do a 1031 exchange for another rental property for which you are the sole owner?

Thank you.  I have not yet completed the purchase for the other real estate property (which I intend to use as my primary residence).  I have also not yet signed the contract to sell the current property that my brother and I own.

Yiou cannot defer the capital gain, since you are not doing a Like Kind Exchange.  A rental cannot be exchanged for a personal residence.