general formula (  4)  is preferred, and a joining group repre› sented by the general formula (2) is the most desirable.  Specific examples of preferred core portions of the poly- mer (C21) are shown below.  Examples of this joining group include groups represented  by general formulas (2) to (5) shown below.  116  US 9,104,101 B2  115  In formulas (2) to (5), each of R 101 , R 102 , R 103  and R 104  independently represents a linear, branched or cyclic alkyl  group of  1  to 12 carbon atoms, an aryl group, or a hydrogen  atom, wherein the hydrogen atoms of the alkyl group or the  aryl group may each be substituted with a halogen atom, an  alkoxy group or an epoxy group. R $^{105 }$represents a linear,  branched or cyclic alkylene group ofl to 12 carbon atoms, an  arylene group, or a single bond, wherein the hydrogen atoms  of the alkylene group or the arylene group may each be  substituted with a halogen atom, an alkoxy group or an epoxy  group.  In the above general formulas (2) to  (5), the alkyl group for  R $^{101 }$to  R $^{104 }$contains  1  to 12 carbon atoms, is preferably a  linearor branched alkyl group, and is most preferably an ethyl  group or a methyl group.  The aryl group preferably contains  6  to 20 carbon atoms,  and specific examples include a phenyl group and a naphthyl  group.  Examples of the halogen atom with which a hydrogen atom  of the alkyl group or aryl group may be substituted include a  fluorine atom, chlorine atom, bromine atom and iodine atom,  and a fluorine atom is particularly desirable.  The alkoxy group with which a hydrogen atom of the alkyl  group or aryl group may be substituted preferably contains  1  to 5 carbon atoms, and is more preferably a methoxy group,  ethoxy group, n-propoxy group, iso-propoxy group, n-butoxy  group or tert-butoxy group.  R $^{101 }$and  R  $^{102 }$are preferably both hydrogen atoms.  R  $^{103 }$and  R  $^{104 }$preferably both represent alkyl groups, rep› resent an alkoxy group and an alkyl group, or represent an  alkoxy group and a hydrogen atom.  In the general formula (5), R 105  represents a linear,  branched or cyclic alkylene group of  1  to 12 carbon atoms  which may be substituted with an alkoxy group, hydroxyl  group, halogen atom or epoxy group, an arylene group which  may be substituted with an alkoxy group, hydroxyl group,  halogen atom or epoxy group, or a single bond.  Examples of the halogen atom within  R  105  include the  same halogen atoms as those mentioned above within the  description of  R  $^{101 }$ti  R  104 .  Examples of the alkoxy group within R $^{105 }$include the same 55  alkoxy groups as those mentioned above within the descrip› tion of  R  101 to  R 104 .  Examples of the alkylene group or arylene group for R 105  include groups in which a hydrogen atom has been removed  from the alkyl groups and aryl groups described above for  R $^{101 }$to  R 104 .  Of the above possibilities, R$^{105 }$is preferably an alkylene  group or a single bond.  Among the joining groups represented by the above gen- era! formulas (2) to (5), a joining group represented by the  general formula (2) or a joining group represented by the  Examples of the polymer chains that constitute the arm  portions include the same polymers as those described above  for the component (Cl). For example, specific examples of  polymer chains containing the aforementioned structural  units (a12) and (a32) include polymer chains containing the  two structural units represented by general formula (P-1)  shown below.  The polymer chains bonded to the core portion may be the  same or different from each other, but are preferably the same,  as such compounds yield superior effects for the present  invention.  These polymer chains that are bonded to the core portion  are preferably bonded to each of the terminals of the core  portion (namely, the terminals of  X 21  on the opposite side  from  X $^{22 }$in the above formula  (1  )).  The arm portions of the polymer (C21) are composed of  polymer chains that are bonded to the core portion described  above.  (Arm Portions)  (1-2)  (1-1)  i  [Chemical Formula 52]  -R10s-----C(R103)(R104)---0-----C(=O)- (5) -S-----C(R 101 )(R 102 )---0- (4)  -S-----C(R101)(R102)-S- (3)  -O-----C(R101)(R102)---0- (2) 