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## Cobordism theory of semifree circle actions on complex n-spin manifolds.

Doctor of Philosophy / Department of Mathematics / Gerald H. Hoehn / In this work, we study the complex N-Spin bordism groups of semifree circle actions and

elliptic genera of level N.

The notion of complex N-Spin manifolds (or simply N-manifolds) 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 N-Spin 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 N-Spin 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.

Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/12031 |

Date | January 1900 |

Creators | Ahmad, Muhammad Naeem |

Publisher | Kansas State University |

Source Sets | K-State Research Exchange |

Language | en_US |

Detected Language | English |

Type | Dissertation |

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