Andrew Yang made a splash last week when he entered the mayor’s race and injected energy into what had been a relatively calm and polite campaign season.

Other campaigns pounced on Mr. Yang, questioning his authenticity as a New Yorker and his commitment to the city. While their excavations highlighted some of his weaknesses, they also revealed how the candidates view Mr. Yang as a threat.

The campaigns also released their fundraising numbers last week, showing which candidates are in the strongest financial position while a former Wall Street executive, known for a #MeToo complaint, stepped into the lesser-known Republican field.

Here are some key developments in the race:

Even before Mr. Yang even entered the race, he had made fun of a comment on social media to the New York Times explaining his decision to leave New York City for his Hudson Valley weekend home at the start of the pandemic.

That was before the bodega incident.

The day after Mr. Yang ran a personal campaign launch in Morningside Heights, he posted a video on Twitter about his love for bodegas – a safe stance few would question. But Mr. Yang recorded the video in a spacious, glitzy shop that few New Yorkers would consider a bodega.

The video got Mr. Yang more ridiculed – and 3.7 million views by Sunday afternoon.

Rival campaigns took other blows on him. After Mr. Yang finished a tour of the Brownsville neighborhood of Brooklyn, the campaign by Eric Adams, president of the Brooklyn borough, said, “Eric doesn’t need a tour of Brownsville. He was born there. “

The campaign manager of Maya Wiley, a former attorney for Mayor Bill de Blasio, threw Mr. Yang’s evasive maneuver from the presidential campaign to the New York Mayor’s race: “Maya is running – not as a backup plan – but because she has devoted everything to life to improve, empower, and uplift the New Yorkers. “

Mr. Stringer’s campaign spokesman, Tyrone Stevens, also dug: “We welcome Andrew Yang to the Mayor’s Race – and to New York City.”

The choice of music for an official launch or acceptance speech for a candidate is usually a calculated decision. Fleetwood Mac’s “Don’t Stop” was Bill Clinton’s 1992 campaign theme song; Lordes “Royals” preceded Mr de Blasio’s 2013 victory speech.

Mr. Yang came to his kick-off event in Morningside Park in Manhattan and danced to the Drake song “God’s Plan,” which includes the lyrics, “They Wish Me / Bad Things.”

Indeed, Mr. Yang was faced with a flurry of questions from journalists about why he had left town during the pandemic and why he had not voted in local elections. An important question is whether Mr. Yang sees the job as a stepping stone to running for national office again – like Mr. de Blasio, who received criticism for his poor offer for president in 2019 and several trips to Iowa.

When asked by the New York Times whether he would pledge not to run for president during his tenure as mayor, Mr. Yang declined. But he said being Mayor of New York would be the job of a lifetime.

“New Yorkers have nothing to fear,” he said.

Mr. Yang made a suggestion that the city should take control of the subway away from the state. There is only one obstacle: Governor Andrew M. Cuomo, who has taken near complete control of the transit agency and is not known to relinquish power.

“Who knows? Maybe he’ll be happy when the city takes it out of his hands,” Yang said to reporters who had gathered on a subway platform and laughed in disbelief at the thought.

He spent his first day campaigning through four of the city’s five counties (sorry, Staten Island). At NY1’s Inside City Hall that evening, Mr. Yang disappointed some by saying the city may not close the Rikers Island prison by 2027.

“Rikers Island should be closed but we need to be flexible on the timeline,” he said.

Mr. Yang pointed to an important confirmation when he came on the trail: Representative Ritchie Torres of the Bronx, a rising star in the Democratic Party who helped counter criticism that Mr. Yang had no contact with the city.

Mr. Torres and Mondaire Jones are the first openly gay black men to serve in Congress, and Mr. Torres has been campaigned for. He had met or had conversations with Ms. Wiley, Mr. Adams, Mr. Stringer, Raymond J. McGuire, and Shaun Donovan, a former housing secretary under President Barack Obama.

Mr Torres said he gave the lost campaigns a heads up on his decision, despite being intrigued by the vote on the indictment against President Trump.

“No mayoral candidate supported me in my race,” said Torres. “I didn’t owe anyone anything.”

Mr. Torres said Mr. Yang’s endorsement of a universal basic income would be a victory for the South Bronx county, which he represents, one of the poorest in the nation. He said that he also likes the fact that Mr. Yang is not part of the city’s political establishment.

The confirmation enables Mr. Torres to coordinate with a moderate progressive colleague. If Mr. Yang wins, it would strengthen Mr. Torres’ standing and give him a powerful ally in the town hall.

When asked about the response to his decision, Torres said, “Eric Adams was friendly, most were disappointed, and one campaign was particularly hostile.”

Several people familiar with the discussions said the McGuire campaign responded with hostility. Mr. Torres met with Mr. McGuire, a former Wall Street executive, at an event in the Hamptons this summer, and his campaign believed they had the inside track.

Mr. McGuire’s campaigning denied being upset about the nudge.

“Ray is not a politician and has no grudge,” said his spokeswoman Lupé Todd-Medina. “He looks forward to working with the congressman when he’s mayor.”

Many officials who have worked in and around the city government appreciate Kathryn Garcia, the city’s former sanitation commissioner who, as a trusted manager, is able to help drive the city’s recovery from the pandemic. But she falls behind in the money race.

Ms. Garcia raised approximately $ 300,000 and did not qualify for any public matching funds.

However, recent records showed that Ms. Garcia received campaign contributions from a number of high-ranking New Yorkers, including Joseph J. Lhota, the former head of the Metropolitan Transportation Authority, who ran as Republican against Mr. de Blasio in 2013. Polly Trottenberg, the city’s former traffic commissioner; and Kathryn Wylde, the head of a prominent group of companies. Ms. Wylde also donated to Mr. McGuire, who is popular among Wall Street donors.

Monika Hansen, Ms. Garcia’s campaign manager, said that many city employees support her offer.

“Kathryn has the support of the makers of the New York government at every rank,” she said.

A lesser-known candidate, Zachary Iscol, a nonprofit leader and former Marine, has raised nearly $ 750,000 and expects to soon qualify for the relevant funds.

Another candidate who worked in Mr de Blasio’s administration is struggling: Loree Sutton, a former veterans affairs commissioner who has $ 398 on hand and $ 6,000 in outstanding debt. She said her campaign has had some problems but is reorganizing and “is in this race and in to win it”.

The democratic primary in June is expected to decide the mayor’s race. The registered Democrats in New York City are far more numerous than the Republicans. But there’s also a Republican primary in June, and a new candidate entered the race last week: Sara Tirschwell, a former Wall Street executive who once filed a #MeToo complaint against her boss.

In an interview, Ms. Tirschwell referred to her experience as a single mother and moderate Republican with liberal social views. She highlighted her “leadership skills” as a rare woman who held high positions in financial companies.

“I think there is a need for a moderate in this race, and it’s not clear that a moderate will survive a Democratic elementary school in New York City,” she said.

Ms. Tirschwell, who grew up in Texas, echoed the complaints of many Republicans – and some Democrats – that “Bill de Blasio is probably the worst mayor in our lives.” But she didn’t want to talk about the recent violence in Washington or the impeachment of Mr Trump.

“This race is about New York, and it’s about New Yorkers and the crisis this city is facing, and that’s what my campaign is focusing on,” she said.

Other names that have popped up in Republican Elementary School: John Catsimatidis, the billionaire of the Gristedes grocery chain; Fernando Mateo, a taxi driver attorney linked to a scandal surrounding Mr de Blasio’s fundraiser; and Curtis Sliwa, the founder of the Guardian Angels.