There was no safe way across the thick slab of ice on the sidewalk.

So William Sullivan, 56, shuffled forward a foot at a time, feeling around for soft spots as he tried to avoid the slick areas that would take him down. He made it, that time. His 84-year-old neighbor was not so lucky; he fell last month going to the corner bodega for coffee, and he still has back pain.

In the Longwood neighborhood of the Bronx, the ice has become a dreaded daily obstacle. On a busy strip of East 167th Street last week, it covered about 15 yards of sidewalk, in front of two vacant, boarded-up houses. No one cleans up that stretch of sidewalk after a snowfall, and as winter wears on, the ice grows ever thicker and more treacherous, residents say. And while New York City authorities have issued tickets to the buildings’ owners, the city will not clear the ice.

In the city, where walking is a way of life, keeping sidewalks clear in the winter is not merely a neighborly courtesy, it is also required under the law. Businesses, homeowners and others in charge of properties are given four hours from the time snow has stopped falling (longer if it ends at night) to clean the pavement. Failure to do so can result in tickets carrying fines of $100 to $150 for a first offense and up to $350 for multiple violations.

The Sanitation Department has issued more than 10,000 tickets this winter and more than 42,000 tickets since 2010, according to a New York Times analysis of city data. In total, those tickets carried fines of nearly $8.5 million (excluding a small percentage of tickets that were successfully challenged), of which just $2.6 million has been paid so far.