* Graphic: sterling and gilt yields bit.ly/2dgAXn1
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv
By Jemima Kelly
LONDON, Dec 4 (Reuters) - Sterling slipped against a stronger dollar on Monday but edged up against the euro, with investors focused on a summit in Brussels, where British Prime Minister Theresa May hopes to break a deadlock in Brexit talks with a new divorce offer.
Over lunch with European Commission President Jean-Claude Juncker and European Union Brexit negotiator Michel Barnier, May will try to persuade them to start discussions on a new trade pact and a two-year transitional deal.
EU officials and diplomats say they are increasingly optimistic a deal can be struck, and so are investors: a Reuters poll last week found economist believe the chance of a disorderly Brexit has declined over the past month.
Such optimism drove sterling to six-month highs on a trade-weighted basis last week and to its highest in two months against the dollar at $1.3550.
And speculators bought back into the pound in the week up to last Tuesday, data showed on Friday, with positioning moving into positive territory - reflecting more bets that sterling will strengthen than that they will fall - for the first time since October.
“Strong signals could emerge later today as to whether EU negotiators are recommending to EU leaders that Brexit negotiations should move to Phase II ... We think sterling can outperform, but prefer gains versus the euro or yen,” said ING currency strategist Chris Turner.
Sterling slipped to $1.3442 on Monday, down 0.3 percent on the day. Against the euro, it was 0.1 percent stronger at 88.27 pence.
Traders were also focused on the latest activity data from the construction sector, due at 0930 GMT.
Editing by Larry King