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Topology and Dynamics: Rokhlin Memorial
August 19-25, 1999
Steklov Institute of Mathematics at St. Petersburg
St. Petersburg, Russia

Organizers
N. Netsvetaev, A. Vershik, O. Viro

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Quadratic property of the Kervaire semicharacteristic
by
Semen S. Podkorytov
Steklov Institute of Mathematics at S.Petersburg

\1 1

Fix n=4m+1. If X is a closed oriented n-manifold, the residue
\k(X)= 2m
å
i=0 
 dimHi(X;\Q) mod 2 in \Z2
is called the rational Kervaire semicharacteristic of X. Fix a smooth manifold V. Let E be the set of germs of oriented n-submanifolds of V. Let F be the vector space of all \Z2-valued functions on E. For an oriented n-submanifold X subset V let \1X in F be the characteristic function of the set of germs of X. It is proven that there exists a quadratic form q F --> \Z2 such that for any closed oriented n-submanifold X subset V one has
\k(X)=q(\1X).

Date received: August 11, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacy-49.