-bordism: structure results and geometric representatives. (June 2019)

• Record Type: Journal Article
• Authors: Limonchenko, I. Yu.; Panov, T. E.; Chernykh, G. S.
• Is Part Of: Russian mathematical surveys. Volume 74:Number 3(2019)
• Page Start: 461
• Page End: 524
• Publication Date: 2019-06
• Subjects: 55N22 -- 57R77; 55T15 -- 14M25 -- 14J32; special unitary bordism -- $SU$-manifolds -- Chern classes -- toric varieties -- quasi-toric manifolds -- Calabi–Yau manifolds; Mathematics -- Soviet Union -- Periodicals; Mathematics -- Russia (Federation) -- Periodicals; Mathematics -- Periodicals; Mathematicians -- Soviet Union -- Periodicals; Mathematicians -- Russia (Federation) -- Periodicals; 510.5
• DOI: 10.1070/RM9883
• Languages: English
• ISSNs: 0036-0279

Abstract

Abstract: The first part of this survey gives a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner–Floyd, Wall, and Stong with the Adams– Novikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 paper of Novikov. In the second part toric topology is used to describe geometric representatives in -bordism classes, including toric, quasi-toric, and Calabi–Yau manifolds. Bibliography: 56 titles.