Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A class of $ 4$-manifolds which have $ 2$-spines

Author: Bruce Trace
Journal: Proc. Amer. Math. Soc. 79 (1980), 155-156
MSC: Primary 57Q99; Secondary 57Q15
MathSciNet review: 560603
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we establish the following.

Theorem. Let $ {M^4}$ denote a piecewise linear or smooth compact 4-manifold-with-boundary having a handle decomposition consisting of 0-, 2- and 3-handles. Then $ {M^4}$ has a 2-dimensional spine if and only if $ {H_3}({M^4}) = 0$.

References [Enhancements On Off] (What's this?)

  • [1] Marvin Greenberg, Lectures on algebraic topology, Benjamin, New York, 1967. MR 0215295 (35:6137)
  • [2] C. P. Rourke and B. J. Sanderson, Introduction to piecewise linear topology, Springer-Verlag, Berlin and New York, 1972. MR 0350744 (50:3236)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57Q99, 57Q15

Retrieve articles in all journals with MSC: 57Q99, 57Q15

Additional Information

Keywords: Handle presentation, i-handle, k-spine, complementary handles
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society