Can an HDMI cable carry a mouse a keyboard signal?

I would like to plug a mouse and keyboard into a monitor and have the HDMI cable carry the signal back to the laptop along with the video. Do HDMI cables an ports support this functionality?

The laptop—an Acer Aspire V5-571P-6828 running Windows 10—has an HDMI port but no other video ports, so a DisplayPort is not an option.

No, HDMI cables don't support this functionality.

HDMI does have a backchannel (CEC) which in principle could be used to carry mouse and keyboard signals, but I don't know of any hardware which actually uses it for that. You may be able to use it that way in hardware you built yourself, but it's extremely unlikely your monitor supports it.

Monitors sometimes have an integrated USB hub for mouse and keyboard, and require an USB cable back to the computers.