Spelling suggestions: "subject:"fordism 1heory"" "subject:"fordism atheory""
1 
Cobordism theory of semifree circle actions on complex nspin manifolds.Ahmad, Muhammad Naeem January 1900 (has links)
Doctor of Philosophy / Department of Mathematics / Gerald H. Hoehn / In this work, we study the complex NSpin bordism groups of semifree circle actions and
elliptic genera of level N.
The notion of complex NSpin manifolds (or simply Nmanifolds) was introduced by Hoehn
in [Hoh91]. Let the bordism ring of such manifolds be denoted by
U;N and the ideal in U;N Q generated by bordism classes of connected complex NSpin manifolds admitting
an e ffective circle action of type t be denoted by IN;t. Also, let the elliptic genus of level n
be denoted by 'n. It is conjectured in [Hoh91] that IN;t = \ njN n  tker('n):
Our work gives a complete bordism analysis of rational bordism groups of semifree circle
actions on complex NSpin manifolds via traditional geometric techniques. We use this
analysis to give a determination of the ideal IN;t for several N and t, and thereby verify the
above conjectural equation for those values of N and t. More precisely, we verify that the
conjecture holds true for all values of t with N 9, except for case (N; t) = (6; 3) which
remains undecided. Moreover, the machinery developed in this work furnishes a mechanism
with which to explore the ideal INt
for any given values of N and t.

Page generated in 0.0246 seconds