On realizing homology classes by maps of restricted complexity

Mark Grant*, Andras Szucs

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
10 Downloads (Pure)


We show that in every codimension greater than 1, there exists a mod 2 homology class in some closed manifold (of sufficiently high dimension) that cannot be realized by an immersion of closed manifolds. The proof gives explicit obstructions (in terms of cohomology operations) for realizability of mod 2 homology classes by immersions. We also prove the corresponding result in which the word 'immersion' is replaced by 'map with some restricted set of multi-singularities'.

Original languageEnglish
Pages (from-to)329-340
Number of pages12
JournalBulletin of the London Mathematical Society
Issue number2
Early online date14 Nov 2012
Publication statusPublished - Apr 2013


  • self-intersections
  • singularities
  • immersions
  • spaces


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