NOVELTY - A polymer (P1) obtained by polymerizing: a polymerizable compound (I) or (II); a compound (III); and a compound (IV), is new.    USE - In an electrolytic solution for a lithium secondary battery (claimed) useful for notebook computers, or cellular phones.    ADVANTAGE - The polymers provide a non-aqueous electrolytes and battery having excellent balance between energy density and battery characteristics while improving safety. The polymers provide electrolytes with improved safety during overcharge without degrading the performance of a battery.    DETAILED DESCRIPTION - A polymer (P1) obtained by polymerizing: a compound of formula Z1-X-A (I) or Z1-A (II); a compound of formula Z2-Y1 (III); and a compound of formula Z3-W1 (IV), is new.    Z1-Z3=polymerizable functional group;    X=1-20C hydrocarbyl or 1-20C oxyalkylene;    A=aryl functional group;    Y1=highly polar functional group;    W1=less polar functional group.    INDEPENDENT CLAIMS are included for the following:    (1) new polymer (P2) having a formula -(Zp1-X-A)a-(Zp2-Y1)b-(Zp3-W1)c- (V), or -(Zp1-A)a-(Zp2-Y1)b-(Zp3-W1)c- (VI);    (2) a lithium secondary battery comprising a cathode, an anode, and an electrolyte, where the electrolyte contains the polymer (P1) or (P2);    (3) an electrolytic solution (S1) for a lithium secondary battery, containing the polymer (P1) or (P2);    (4) an overcharge inhibitor for a lithium secondary battery, containing the polymer (P1) or (P2) as an active component;    (5) preparation of the polymer (P1);    (6) a charge control method for a lithium secondary battery involving: using the electrolytic solution (S1), determining a completion of charging by detecting an increase in overvoltage, and terminating the application of voltage; and    (7) a lithium secondary battery containing the electrolytic solution (S1), having a control unit which determines a completion of charging by detecting an increase in overvoltage and terminates an application of voltage.    Zp1-Zp3=residue of a polymerizable functional group;    a-c=mol %.