A Series of Elements of Order 4 in the Symplectic Cobordism Ring

Abstract

A series of elements of order 4 in the symplectic cobordism ring is constructed.

Symplectic cobordism in small dimensions and a series of elements of order four

“…The present work was finished in the middle of 90-ties and the main result was announced in [44]. About the same time there appeared the works of B. I. Botvinnik and S. O. Kochman [8], [9] asserting the existence of higher torsion in M Sp * .…”

Adams spectral sequence and higher torsion in $MSp_*$

“…The symplectic cobordism ring MSp * is the homotopy of the Thom spectrum MSp and classifies up to cobordism the ring of smooth manifolds with a symplectic structure on their stable normal bundles. Although MSp * only has two-torsion, its ring structure is very complicated and is only completely understood through the 100 stem [7], [13], [15]. In [2], we proved that there are nontrivial elements in MSp * of all orders 2 k .…”

Characteristic classes and transfer relations in cobordism

“…nonoriented (O(n)), oriented (SO(n)) and complex (U(n)) -the structure of its coefficient ring remains largely unknown. In the study of symplectic cobordism various methods have been applied: the classical Adams spectral sequence [14], the Adams-Novikov spectral sequence [18,20], the Atiyah-Hirzebruch spectral sequence [16], the use of characteristic classes and generalizations of formal groups [15,5], and cobordism with singularities [19]. In this paper we apply the transfer maps to the study of the symplectic cobordism ring.…”