They're swilling Google-tinis in Sarasota, and vowing to Google-ize the names of their firstborn children up in Duluth.

SAN JOSE, Calif. — They’re swilling Google-tinis in Sarasota, and vowing to Google-ize the names of their firstborn children up in Duluth.

Topeka has been temporarily re-christened Google, Kansas. And mayors throughout the realm are vying for the search giant’s favor, from sucking up to it on Twitter to jumping into icy Lake Superior in their shorts.

All this to convince Google to bring lightning-quick Internet access to their communities.

From Berkeley to Boca Raton, hundreds of cities have joined the high-tech stampede to be chosen as a host for Google’s grand fiber-optic experiment — the free installation of a network delivering Internet speeds 100 times faster than what most Americans have ever seen.

Unlimited Digital Access. $1 for 4 weeks.

“The whole country is going goo-goo over Google,” says Josh Wallace with the city of Palo Alto, Calif., which, by the way, is also courting Google for a slice of the fiber pie. “If I were Google, I’d look very hard at Palo Alto. We’ve got a lot of Facebook employees living here, and these engineers are crawling out of their skin to access this kind of network.”

Crawling out of one’s skin would simply be the latest stunt by Americans craving warp-speed Internet. Google, which would benefit from faster search capabilities and the advertising that would bring, first dangled the red meat on Feb. 10, when the announcement was made that it was “planning to build and test ultrahigh speed broadband networks in a small number of trial locations across the country.”

Google would pay for installation, running cable under or above ground to every business and home in a host community.

It would be an “open access” network that service providers like phone and cable companies could piggyback on and then compete for customers.

Communities across America found the offer too good to refuse.

Duluth, Minn., Mayor Don Ness was the first to literally jump.

“At first, I had no interest in doing it,” Ness said of his publicity-milking plunge last month into Lake Superior. “The temperature’s about 35 degrees, but I grew up here and it’s actually not that much colder than jumping in in early June. You just need to look beyond the ice floating on the surface.”

Inspired by Ness’ derring-do and Topeka’s brainstorm to name itself Google for the month of March, the country was off and running toward the fiber-optic gold mine.

In Highlands Ranch, Colo., boosters were planning to get residents to form a human “We Love Google” sign at a local high school football stadium.

Baton Rouge, La., deputy mayor John Carpenter said the city would not lower itself to the circus antics other places have used to pump up the natives and get Google to take notice.

“We think at the end of the day it’s not the gimmicks that’ll persuade Google, but the strength of our application. We don’t think you need to jump in a lake to get noticed.”