HODGE CONJUCTURE DEFEND AND NEGATION solution

the Hodge conjecture asserts that the basic topological information like the number of holes in certain geometric spaces, complex algebraic varieties, can be understood by studying the possible nice shapes sitting inside those spaces, which look like zero sets of polynomial equations. The latter objects can be studied using algebra and the calculus of analytic functions, and this allows one to indirectly understand the broad shape and structure of often higher-dimensional spaces which can not be otherwise easily visualized. my soltuion negation:-> basic topology information like the numebr of holes with polynomial time (h,t) in certain gemotric spaces complex alagbric varities that differ from static times ,can be udnertsood by studying by time shape(time topology) and can only understood by time topology space which look like time polynomial states. latter objects can be studeied by time compllexity algebra and the calculas of analytic fucntiom and this allow one to indireclty understood the broad shape and structure with static time of their shappe even high dimnestional spaces whcih can not be otehr wise ealsily visualized when we take a time as the confficient varaible then na dtime is polynomial states then by that genmertic space ,complex algebric verities that differ by static time that may differ in time space complexity if teh tiem ahve cocorridnet then all complex varainats will come in differnt tiem complexity so we too space with the time topology if there is not time hole in ceratin gematric space then there snot be hole taht is connetced that is non conentced surface one srafce of time and one surafce of holes so ther si not rreason that with desimailr time they insert the nice shape sitting isndie those shapes if polynomial of time is working. if time topological information like the numebr of holes in certain time genotric sapce ,complex alagbric varities can be undrstood by studyinng topoligcla information like numebr of holes in certain gemteric spaces ,complex algebtric varieties then ca be udnerstod by studying the posible nice shapes sitting inside thsoe sapces but randmly whne time space will conevrt in different time sapces then also these ncie shapes cant sisttin isndie thsoe sapce by time topology