The Tulane men’s basketball team is on edge.

A combination of missed opportunities and stunted momentum has Tulane in a sour mood as it completes its three-game homestand Tuesday at 6 p.m. against Tulsa in Devlin Fieldhouse.

Just a week after jumping to its best conference record in seven years, Tulane’s season suddenly is teetering on the edge of irrelevance. After a dispiriting 66-52 loss to SMU on Wednesday, the Green Wave (13-7, 4-4 American) watched its chance to sweep Memphis fade away in the final 5 seconds of Saturday night’s 57-55 defeat in the Smoothie King Center

“We just have that edge about us,” junior guard Louis Dabney said. “We just feel like this next game is a must-win. We just need to control our homecourt, and we need this game to just get back on track to how we were playing in the earlier part of conference and to prove a point.”

It will be a difficult point to make. With the AAC’s current No. 1 seed, the Golden Hurricane (14-5, 7-0), making its way to New Orleans, there’s a palpable sense that Tulane is facing a potential crossroads. Not only is it trying to avoid a three-game home losing streak, it’s also trying to keep pace in an increasingly competitive league that pushed the Green Wave from second place to seventh in just two games.

While coach Ed Conroy insisted his team’s resilience is beyond question and improvement is taking place on the floor, there’s added pressure to turn some of those positive feelings into victories.

“We want to get back out there because we feel like we owe somebody something,” senior guard Jay Hook said. “We just want to hold it down against Tulsa, who is the No. 1 team in the conference and gives us something to prove. We try not to think about the losses (to Memphis and SMU), but you want to hold that grudge and not let that feeling go. It’s about taking it into practice, so not thinking about the loss necessarily, but using the feeling of losing to keep you focused.”

It’s a feeling Tulsa is unfamiliar with in 2015. After starting the season an inauspicious 5-5, bottoming out in losses to Southeastern Oklahoma State and Oral Roberts, it didn’t appear Tulsa was on the path to the top of the AAC.

Instead, under new coach Frank Haith, Tulsa has gathered steam. Haith, who formerly was coach at Missouri and Miami, focused his game plan on the backcourt combo of James Woodard and Shaquille Harrison.

The pair ranks second and third among the AAC’s scoring leaders, combining to average 31 points. They present the type of challenge Tulane feels it’s properly prepared for.

Conference losses to Memphis, SMU and Temple were largely the result of powerful post teams overwhelming the undersized Green Wave. The fulcrum point of this matchup, though, will come where Tulane is at its best: in the backcourt.

Dabney, Hook and point guard Jonathan Stark will be heavily relied upon to avoid turnovers in an attempt to short-circuit Tulsa’s dangerous transition game. Offensively, it also will need to be more efficient after converting just 33 percent of its shots in each of the past two games.

“It’s still all about that edge,” Hook said. “Tulsa poses a big challenge for us and we, in the backcourt, will have to share our energy and make sure not to take off any plays. A lot of times Tulsa takes advantage because they’re so aggressive and always pushing.

“So it’s all about getting back out there and putting it right to them and making sure no one backs down at any time.”

Women visit Houston

After Sunday’s 64-45 loss at South Florida, the Tulane women continue their road swing with a 7 p.m. Tuesday matchup at Houston.

Sunday’s game was a battle for second place in the AAC behind Connecticut, but the challenge against Houston is a little less daunting. Tulane (15-4, 6-2) handled Houston (6-13, 1-7) 70-40 on Dec. 30 at Devlin; Danielle Blagg led the way with 14 points.