## Pacific Journal of Mathematics

### Vector bundles over $(8k+3)$-dimensional manifolds.

Tze Beng Ng

#### Article information

Source
Pacific J. Math., Volume 121, Number 2 (1986), 427-443.

Dates
First available in Project Euclid: 8 December 2004

https://projecteuclid.org/euclid.pjm/1102702442

Mathematical Reviews number (MathSciNet)
MR819199

Zentralblatt MATH identifier
0574.57010

Subjects
Primary: 57R25: Vector fields, frame fields
Secondary: 55S45: Postnikov systems, $k$-invariants

#### Citation

Ng, Tze Beng. Vector bundles over $(8k+3)$-dimensional manifolds. Pacific J. Math. 121 (1986), no. 2, 427--443. https://projecteuclid.org/euclid.pjm/1102702442

#### References

• [6] Applications. 6.1. Let M = S+Sk X P2/ + 1for k > 0, / > 0. Then we have THEOREM. San(M) > 8. Proof. Plainly Hn~5{M) Hn~6(M) = 0, w4(M) = 0 and 2(M) =
• [11] M immersesin R2""7. Consequently we have by Theorem 5.8: THEOREM 6.4. SupposeM is 4-connected mod 2 and dim M = n = 11 m o d l 6 > l l .Then M immerses in R2n~7if Sq2 Hn~\M\Z) = Sq2 H"-(M) and immerses inR2n~s if Sq2Sq H"-\M)= Sq2Hn~\M). Similarly we have by Theorem 5.7: THEOREM 6.5. Suppose M satisfies conditions A and B 6>/3,w4(M) = 0 and n = ll mod 16 > 11. // Sq1 H\M)= Sq2 H\M)= 0 and if either Sq4 Hn~\M)= 0 or 3H\M) = 0 and Sq2 Hn\M)= 0 /e f /m- merses in R2"~8.
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