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ON INTEGERS OCCURRING AS THE MAPPING DEGREE BETWEEN QUASITORIC 4-MANIFOLDS

Part of: Complex manifolds Operations and obstructions Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  23 December 2016

ÐORÐE B. BARALIĆ
ÐORÐE B. BARALIĆ*
Affiliation:
Mathematical Institute SASA, Kneza Mihaila 36, p.p. 367, 11001 Belgrade, Serbia email djbaralic@mi.sanu.ac.rs
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Abstract

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We study the set $D(M,N)$ of all possible mapping degrees from $M$ to $N$ when $M$ and $N$ are quasitoric $4$-manifolds. In some of the cases, we completely describe this set. Our results rely on Theorems proved by Duan and Wang and the sets of integers obtained are interesting from the number theoretical point of view, for example those representable as the sum of two squares $D(\mathbb{C}P^{2}\sharp \mathbb{C}P^{2},\mathbb{C}P^{2})$ or the sum of three squares $D(\mathbb{C}P^{2}\sharp \mathbb{C}P^{2}\sharp \mathbb{C}P^{2},\mathbb{C}P^{2})$. In addition to the general results about the mapping degrees between quasitoric 4-manifolds, we establish connections between Duan and Wang’s approach, quadratic forms, number theory and lattices.

Keywords

mapping degreequasitoric manifoldsquadratic formsintersection form

MSC classification

Primary: 55M25: Degree, winding number
Secondary: 55S37: Classification of mappings 32Q55: Topological aspects of complex manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 103 , Issue 3 , December 2017 , pp. 289 - 312
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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