Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $V$ be a vector bundle (with a chosen metric) over a finite CW-complex $X$ and $B(V), S(V)$ the associated (unit) disk resp. sphere bundles. In the paper Clifford-Modules the authors remark that $(B(V),S(V))$ cannot be obtained as a relative CW-complex in an "obvious" way.

I suspect however that B(V) that can be built up from S(V) by attaching cells (in no particular order). The absolute case is a lemma in hatchers k-theory book, but i am not sure if the inductive proof over the cells of $X$ works in the relative case, since checking this formally seem extremly tedious. But maybe someone here has already dealt with a similar issue.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.