– No. I’m sure it’s not. Go on.

– I’m in the media. I buy advertising space for big campaigns.

– So what are you doing in Milan? Are you on holiday?

– No, he says. I’m living out here, temporarily. Doing some work. Staying in a hotel. I’m thinking about going out for dinner, then maybe to a bar. But it’s no fun on your own …

The ellipsis suggests he’s inviting a compliment. I remind myself I still need to find out if he meets people he chats to, and what he does with them if so.

I try to imagine how Jayne might reply. At the very least she’d have to make a reference to what he’d said.

– I bet you wouldn’t be lonely for long, I say.

– Thanks, he replies, and then another message comes through.

– Can I ask what you’re wearing?

So polite, I think. It’s not what I might’ve expected.

But then what did I expect? This is the way it goes, apparently. What are you wearing? Describe it to me. I want to take it off, tell me how it feels. But much sooner, within a few messages, not over a couple of days.

– Why do you want to know?

I wonder if I ought to add a winking face. Is that what Kate would’ve done?

– I just want to be able to picture you.

I feel myself tense. I’m not sure I want him to picture me. It leaves an unpleasant taste. I remind myself I’m doing this for Kate’s sake, and for Connor’s. For all of us.

– If you must know, I type, I’m wearing jeans. And a shirt. Your turn.

– Well, I’m just lying here on the bed.

I look again at his photo and picture him. I see the hotel room, bland and corporate. I wonder if he’s taken his clothes off. I imagine he has a good body, strong and muscular. He’ll have got himself a drink; for some reason I picture him with a beer, drinking straight from the bottle. Something within me begins to open up, but I don’t know what it is. Is it because finally I might be getting somewhere, unlocking the riddle of my sister’s murder? Or because a good-looking man has chosen to send a message to me?

– If you’re busy that’s cool. I’ll leave you alone.

– No. I’m not busy.

– Okay. So I’m here, and you’re there. What’re you up for? What’re you into?

I try to imagine what Kate would’ve said.

I can’t.

– I’m not sure.

– Are you okay?

I decide it’s easier to tell the truth.

– I’ve never done this before.

– No problem. We can chat another time, if you’re uncomfortable?

– No. I’m not uncomfortable. I just don’t want to disappoint you.

– You’re beautiful. How could you disappoint me?

Deep down, but unmistakably there, there’s a weak throb of excitement. A distant signal from the remotest star.

– Thank you.

A moment, then he replies:

– It’s a pleasure. You are beautiful. I’m enjoying talking to you.

– I’m enjoying talking to you, too.

– Why don’t you tell me what you’re doing this evening?

I stop to think. Soon I’ll cook our evening meal, then I might sit with a book. But I don’t want to tell him that.

– I might go out, with friends. Or maybe catch a film.

– Nice.

We talk for a little while longer. He asks me what movies I’ve seen recently, we talk about books and music. It turns out we both love Edward Hopper and have tried but failed to finish Finnegans Wake. It’s pleasurable, but I seem to be getting further and further from finding out whether he’s ever chatted to my sister, or was in Paris in February, or even who I remind him of. After a few more minutes he says:

– Well I’d better get ready, go for dinner.

– And then go on to your bar?

– Possibly. Though I’m not sure I can be bothered now.

– How come?

– I might just come back to the room and see if you’re still online.

There’s another tiny shock of pleasure.

– Would you like that?

– I might.

– I’d like to chat again.

I don’t reply.

– Would you?

I stare at the blinking cursor. For some reason I’m thinking of my time in Berlin, in the squat with Marcus and Frosty and the rest; the sensation of both wanting and not wanting something at the same time.

Again I remind myself who I’m doing this for.

– I would.

We end the conversation. I log off and call Anna.

‘How did it go?’

‘I’m not sure.’

‘Did it get sexual?’

‘Not really. No.’

‘It will,’ she says.

‘Listen, will you look at his profile online? Let me know if you recognize him?’

She hesitates. I hear her stand up; she’s moving around her apartment. ‘Of course. But I don’t recognize his name. I don’t think he can be one of the ones Kate met. I suppose it’s possible he’s someone she chatted to.’

‘I need to find out.’

‘Just don’t get your hopes up.’

I won’t, I tell her. We talk some more. After we’ve said goodbye I go back online. I can’t help it. I look at Lukas’s profile, at the photographs he’s uploaded. They look completely ordinary. He’s wearing a checked shirt, open at the neck, his face is broad and handsome, his eyes dark. Did he know my sister? Is it possible?

I read the rest of his profile. He describes himself as athletic, he’s a lover of fun, he enjoys reading, music, eating out. When I scroll down I see there’s a link to his Facebook page. I click on it.

He’s used the same picture there, but I hardly look at it. I navigate straight to his timeline and begin to scroll backwards. I go back as far as February. I have to be sure.

There’s a photo of him, standing in the desert next to a man. They have their arms round each other’s shoulders, in triumph. Uluru is in the background. ‘We finally made it!’ says the caption. When Kate was killed he was in Australia.

It doesn’t mean he didn’t know her, though. I think again of what he said. You remind me of someone.

I send a message to Anna: ‘Checked Facebook. He was in Australia.’

I go to bed. It’s later than I think; Hugh’s turned out the light and is already asleep. He’s left the curtains open for me to undress in the light from the street outside. Before I do I check if anyone’s there, but tonight the street is empty, other than a couple walking arm in arm, looking either drunk or in love, it’s hard to tell. I’m naked when I get into bed; I turn on to my side and look at Hugh, silhouetted in the half-light. My husband, I tell myself, as if I need to be reminded of the fact.

I kiss him gently, on his brow. The night is hot and sticky and I can taste the sweat that’s formed there. I turn on to my other side, away from him. My hand goes beneath the covers, between my legs. I can’t help it. It’s the talk, this afternoon. The chat with the guy online. Lukas. Something has been aroused, some desire that is complicated yet undeniable.

I let it come. I’m thinking of Lukas. I can’t help it, even if it does feel like a betrayal. You’re beautiful, he’d said, and the excitement I’d felt had been instant and pure. I imagine him now, he’s saying it over and over, You’re beautiful, you’re gorgeous, I want you, yet for some reason he changes, becomes Marcus. He’s leading me upstairs, we’re in the squat, we’re going to the room we shared, to the mattress on the floor, to the tangle of bedclothes unmade from the night before. I’ve spent the day here alone, he’s been out. But now he’s back, there’s only the two of us. He’s argued with his family, his mother is distraught, she wants him home. Even just for a few weeks, she’d said, but he knows she means for ever. I tell him I’ll support him, if he goes, if he decides he wants to, but I know he won’t. Not now he’s here, and happy. He kisses me. I imagine the smell of him, his smooth skin, the fuzz of hair on his chest. These details – things that I know are half remembrances and half imaginings, a mixture of fantasy and memory – come, and they lead me somewhere, somewhere where I am strong and in control and Kate is alive and everything will be all right.