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On smooth surgery
Author(s) -
Weinberger Shmuel
Publication year - 1990
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160430507
Subject(s) - mathematics , citation , algebra over a field , combinatorics , pure mathematics , computer science , topology (electrical circuits) , discrete mathematics , library science
Recall that the structure set is: { f: W + M a simple homotopy equivalence, W a Cat manifold}/Cat-isomorphism. In the topological case, one can turn SToP(M) into an abelian group (and in fact, F/Top has an infinite loop space structure, so that the surgery exact sequence is a long exact sequence of abelian groups). For this see [2]. While no such result is yet known for the smooth case, it is reasonable to believe that one can do as much rationally (suitably interpreted) since Top/O has finite homotopy groups. The above is our version. The difficulty' is, of course, that the map