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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0560603-8
MathSciNet review: 560603
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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$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560603-8
Keywords: Handle presentation, i-handle, k-spine, complementary handles
Article copyright: © Copyright 1980 American Mathematical Society

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