Some complex Grassmannian manifolds that do not fibre nontrivially

Ronald John Dave Ferdinands, Purdue University

Abstract

A compact fibering of a finite CW complex X is a fibration $F\to E\to B$ with $E$ homotopy equivalent to X, and $F$ and $B$ homotopically equivalent to finite CW complexes. X is said to be prime if, given a compact fibering of X, either $F$ of $B$ is contractible. In this thesis the following results are proved: (I) $G\sb{4k + 3,3}(C)$ is prime for all positive integers $k$. (II) $G\sb{8k + 4,4}(C)$ and $G\sb{8k + 6,4}(C)$ are prime for all $k\geq 4$. (III) $G\sb{9k + 3,3}(C)$ is prime for all even positive integers $k$, and $G\sb{9k + 6,3}(C)$ is prime for all odd positive integers $k$.

Degree

Ph.D.

Advisors

Schultz, Purdue University.

Subject Area

Mathematics

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