The novel is based on the (fictional) "Everhard Manuscript" written by Avis Everhard which she hid and which was subsequently found centuries later. In addition, this novel has an introduction and series of (often lengthy) footnotes written from the perspective of scholar Anthony Meredith. Meredith writes from around 2600 AD or 419 B.O.M. (the Brotherhood of Man). Jack London writes at two levels, often having Meredith condescendingly correcting the errors of Everhard yet, at the same time, exposing the often incomplete understanding of this distant future perspective.
Meredith's introduction also acts as a deliberate "spoiler" (the term did not yet exist at the time of writing). Before ever getting a chance to get to know Avis and Ernest, how they fell in love or how Avis became politically involved, the reader is already told that all their struggles and hopes would end in total failure and repression, and that both of them would be summarily executed. This gives all that follows the air of a foreordained tragedy. There is still left the consolation that a happy end would come for humanity as a wholeÂ â though hundreds of years too late for Avis and Ernest as individuals; the cruel oligarchy would fall, and the two will be vindicated and respected by posterity as pioneers and martyrs.
The Manuscript itself covers the years 1912 through 1932 in which the Oligarchy (or "Iron Heel") arose in the United States. In Asia, Japan conquered East Asia and created its own empire, India gained independence, and Europe became socialist. Canada, Mexico, and Cuba formed their own Oligarchies and were aligned with the U.S. (London remains silent as to the fates of South America, Africa, and the Middle East.)
In North America, the Oligarchy maintains power for three centuries until the Revolution succeeds and ushers in the Brotherhood of Man. During the years of the novel, the First Revolt is described and preparations for the Second Revolt are discussed. From the perspective of Everhard, the imminent Second Revolt is sure to succeed but, from the distant future perspective of Meredith, we readers realize that Everhard's hopes were to be crushed for centuries to come.
The Oligarchy are the largest monopoly trusts (or robber barons) who manage to squeeze out the middle class by bankrupting most small to mid-sized business as well as reducing all farmers to effective serfdom. This Oligarchy maintains power through a "labor caste" and the Mercenaries. Labor in essential industries like steel and rail are elevated and given decent wages, housing, and education. Indeed, the tragic turn in the novel (and Jack London's core warning to his contemporaries) is the treachery of these favored unions which break with the other unions and side with the Oligarchy. Further, a second, military caste is formed: the Mercenaries. The Mercenaries are officially the army of the US but are in fact in the employ of the Oligarchs.
Asgard is the name of a fictional wonder-city, a city constructed by the Oligarchy to be admired and appreciated as well as lived in. Thousands of proletarians live in poverty there, and are used whenever a public work needs to be completed, such as the building of levee or a canal.
The Manuscript is Everhard's autobiography as she tells of: her privileged childhood as the daughter of an accomplished scientist; her marriage to the socialist revolutionary Ernest Everhard; the fall of the US republic; and her years in the underground resistance from the First Revolt through the years leading to the Second Revolt. By telling the story of Avis Everhard, the novel is essentially an adventurous tale heavily strewn with social commentary of an alternate future (from a 1907 perspective). However, the future perspective of the scholar Meredith deepens the tragic plight of Everhard and her revolutionary comrades.

Question: What did the introduction fortell would happen to Avis and Ernest in the end?
Answer: They would be executed