罗月桐,北京大学

The Borel conjecture considers the obstruction from homotopy equivalence to homeomorphism for aspherical manifolds. The torus is the first computed case of Borel conjecture with the idea of splitting used in the computation. In this talk I will review the basic results of surgery theory and prove the Borel conjecture for torus following Shanneson and Hsiang’s calculation. Moreover, the further Farrell’s splitting for structure set gives us further tools in the proof of more complicated case of Borel conjecture.