By S. K. Donaldson
The final ten years have visible speedy advances within the realizing of differentiable four-manifolds, now not least of which has been the invention of latest 'exotic' manifolds. those effects have had far-reaching outcomes in geometry, topology, and mathematical physics, and feature confirmed to be a mainspring of present mathematical study. This ebook presents a lucid and available account of the trendy research of the geometry of four-manifolds. hence, it will likely be required examining for all these mathematicians and theoretical physicists whose study touches in this subject. The authors current either a radical therapy of the most traces of those advancements in four-manifold topology--notably the definition of latest invariants of four-manifolds--and additionally a wide-ranging remedy of suitable themes from geometry and worldwide research. the entire major theorems approximately Yang-Mills instantons on four-manifolds are confirmed intimately. at the geometric part, the ebook encompasses a new facts of the category of instantons at the four-sphere, including an in depth dialogue of the differential geometry of holomorphic vector bundles. on the finish of the publication different strands of the speculation are introduced jointly within the proofs of effects which settle long-standing difficulties in four-manifolds topology and that are on the subject of the frontiers of present study. Co-author Donaldson is the 1994 co-recipient of the distinguished Crafoord Prize.
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