references.bib

%%% DG-algebras and formality

@article{DGMS,
author={Pierre Deligne and Phillip Griffiths and John Morgan and Dennis Sullivan},
title={Real homotopy theory of Kähler manifolds},
journal={Inventiones math},
volume={29},
year=1975,
pages={245-274}
}

@article{Petersen,
title={Lie, associative and commutative quasi-isomorphism}, 
author={Ricardo Campos and Dan Petersen and Daniel Robert-Nicoud and Felix Wierstra},
year={2020},
volume={1904.03585},
journal={arXiv},
primaryClass={math.RA}
}

@article{Saleh,
title={Noncommutative formality implies commutative and Lie formality},
author={Bashar Saleh},
journal={Algebraic and Geometric Topology},
year={2017},
volume={17},
pages={2523-2542}
}
%https://arxiv.org/pdf/1609.02540.pdf

@article{sformality,
author = {Marisa Fernández and Vicente Muñoz},
year = {2005},
title = {Formality of Donaldson submanifolds},
volume = {250},
journal = {Mathematische Zeitschrift},
pages = {149-175}
}

@article{cartan,
author = {Henry Cartan},
year = {1954},
title = {DGA-algebres et DGA-modules},
journal = {Séminaire Henri Cartan},
volume = {7},
pages = {1-9}
}
% http://www.numdam.org/article/SHC_1954-1955__7_1_A2_0.pdf

@article{kaledin2,
title = {Formality of DG algebras (after Kaledin)},
journal = {Journal of Algebra},
volume = {323},
number = {4},
pages = {878-898},
year = {2010},
author = {Valery A. Lunts},
}
% https://www.sciencedirect.com/science/article/pii/S0021869309006401

@article{kaledin1,
title = {Some remarks on formality in families},
journal = {Moscow mathematical journal},
volume = {7},
number = {4},
pages = {643-652},
year = {2007},
author = {Dmitry Kaledin},
}
% arXiv:math/0509699




%%% A-infinity algebras

@article{AHO,
author={Bruno Vallette},
title={Algebra+Homotopy=Operad},
journal={Symplectic, Poisson, and noncommutative geometry},
volume={62},
year=2014,
pages={229–290}
}

@article{Ext,
author={Di M. Lu and John H. Palmieri and Quan S. Wu and James J. Zhang},
title={A-infinity structure on Ext-algebras},
journal={Pure Applied Algebra},
volume={213},
year=2009,
pages={2017-2037}
}
% https://sites.math.washington.edu/~palmieri/Papers/ext-a-infty.pdf

@article{Merkulov,
author={Sergei A. Merkulov},
title={Strong homotopy algebras of a Kähler manifold},
journal={International mathematics research notices},
volume={3},
year=1999,
pages={152-164}

}
% https://arxiv.org/pdf/math/9809172.pdf

@article{berglund,
author={Alexander Berglund and Kaj Börjeson},
title={Koszul A-infinity-algebras and free loop space homology},
year={2020}, 
journal={Proceedings of the Edinburgh Mathematical Society},
volume={63},
pages={37-65}
}
%https://arxiv.org/pdf/1711.06496.pdf


@book{ab94,
author = {Charalambos D. Aliprantis and Kim C. Border},
year = {1994},
title = {Infinite Dimensional Analysis},
publisher = {Springer verlag}
}


@article{detection,
author={Urtzi Buijs and José Manuel Moreno-Fernández and Aniceto Murillo},
title={A-infinity structures and Massey products},
journal={Mediterranean Journal of Mathematics},
volume={17},
year=2020
}

@article{french1,
author={Kenji Lefèvre-Hasegawa},
title={Sur les A-infinity catégories},
journal={PhD thesis},
volume={University Paris 7},
year=2003,
}
%https://arxiv.org/pdf/math/0310337.pdf

@article{kadeishvili,
author={Tornike Kadeishvili},
title={On the homology theory of fiber spaces},
journal={English translation: Russian math. surveys},
volume={35},
year=1980,
pages={231-238}
}
%In russian: Uspekhi Mat. Nauk 35:3 183-188 (1980), 
   %https://arxiv.org/pdf/math/0310337.pdf

@article{Sagave,
author = {Steffen Sagave},
year = {2010},
title = {DG-algebras and derived A-infinity algebras},
volume = {639},
journal = {Journal für die reine und angewandte Mathematik},
pages = {73–105}
}
% https://arxiv.org/pdf/0711.4499.pdf


@article{transfer,
author = {Martin Markl},
year = {2006},
title = {Transferring A-infinity (strongly homotopy associative) structures},
volume = {79},
journal = {Circolo Matematico di Palermo},
pages = {139–151}
}
% https://arxiv.org/pdf/math/0401007.pdf

@article{sha-example,
author = {Michael P. Allocca and Tom Lada},
title = {A finite dimensional A-infinity algebra example},
journal = {Georgian mathematical journal},
volume = {17},
year = {2010},
pages = {1-12}
}






%%% Model categories

@article{jardine,
author={Rick Jardine},
title={A closed model structure for differential graded algebras},
journal={Fields Institute Communications},
volume={17},
year=1997,
pages={55-58}
   
}
% https://ncatlab.org/nlab/files/JardineModelDG.pdf

@article{monoid,
author = {Stefan Schwede and Brooke Shipley},
year = {2000},
title = {Algebras and modules in monoidal model categories},
volume = {80},
journal = {Proceedings of the London mathematical society},
pages = {491-511}
}
% https://homepages.math.uic.edu/~bshipley/monoidal.pdf

@book{hovey,
author = {Mark Hovey},
title= {Model categories},
publisher= {American Mathematical Society},
year={2007}
}

@book{weibel,
author = {Charles A. Weibel},
title= {An introduction to homological algebra},
publisher= {Cambridge university press},
year={1994}
}

@article{small_objects,
author = {Richard Gardner},
year = {2009},
title = {Understanding the small object argument},
volume = {17},
journal = {Applied Categorical Structures},
pages = {247–285}
}
% https://homepages.math.uic.edu/~bshipley/monoidal.pdf










%%% Massey products

@article{nonformal_loop,
author={Somnath Basu},
title={Of Sullivan models, Massey products, and twisted Pontrjagin products},
year= {2015},
volume = {10},
journal = {Journal of homotopy and related structures},
pages = {239-273}
}
%https://arxiv.org/pdf/1209.3226.pdf

@article{massey,
author = {William S. Massey},
year = {1958},
title = {Some higher order cohomology operations},
journal = {Symposium internacional de topología algebraica},
pages = {145–154}
}
%https://www.maths.ed.ac.uk/~v1ranick/papers/mexico.pdf

@article{four-link, 
author = {Edward J. O'neill},
year = {1979},
title = {Higher order Massey products and links},
volume = {248},
journal = {Transactions of the American mathematical society},
pages = {37-66}
}
% https://www.ams.org/journals/tran/1979-248-01/S0002-9947-1979-0521692-6/S0002-9947-1979-0521692-6.pdf


@article{linking,
author = {William S. Massey},
year = {1998},
title = {Higher order linking numbers},
volume = {7},
journal = {Journal of Knot Theory and Its Ramifications},
pages = {393-414}
}
%https://www.worldscientific.com/doi/abs/10.1142/S0218216598000206

@article{naturality,
author = {James Peter May},
year = {1969},
title = {Matric massey products},
volume = {12},
journal = {Journal of algebra},
pages = {533-568}
}
% https://core.ac.uk/reader/81994620

@article{non_formal1,
author = {Diarmuid Crowley and Johannes Nordström},
year = {2020},
title = {The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3},
volume = {13},
journal = {Journal of topology},
pages = {539-575}
}

@article{non_formal2,
author = {Stephen Halperin and James Stasheff},
year = {1979},
title = {Obstructions to homotopy equivalences},
volume = {32},
journal = {Advances in mathematics},
pages = {233-279}
}
% https://www.sciencedirect.com/science/article/pii/0001870879900434

@book{exact-massey,
author = {Aleksy Tralle and John Oprea},
year = {1997},
title = {Symplectic Manifolds with no Kähler Structure},
publisher = {Springer verlag},
series = {Lecture notes in mathematics},
volume = {1661}
}
% https://link.springer.com/book/10.1007%2FBFb0092608#about













%%% Introduction

@article{Serre,
author={Jean-Pierre Serre},
title={Groupes d’homotopie et classes de groupes
abeliens},
journal={Annals of mathematics},
year=1953,
pages={258-294}
}

@article{Quillen,
author={Daniel Quillen},
title={Rational homotopy theory},
journal={Annals of mathematics},
year=1969,
pages={205–295}
}

@article{Sullivan,
author = {Dennis Sullivan},
title = {Infinitesimal computations in topology},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {269-331},
volume = {47},
year = {1977}
}

@book{MIT,
author={Dennis Sullivan},
title={Geometric topology, Part I: Localization, periodicity, and Galois symmetry},
journal={K-Monographs in Math},
number ={8},
year=2004
}

@book{PLdeRham,
author={Aldridge Bousfield and Victor Gugenheim},
title={On PL deRham theory and rational homotopy type},
journal={Memoirs of the american mathematical society},
number = {179},
year=1976
}













%%% Rational homotopy theory

@article{co-H-space,
author = {Hans-Werner Henn},
year = {1983},
title = {On almost rational co-H-spaces},
number = {87},
journal = {Proceedings of the american mathematical society},
pages = {164-168}
}
% https://www.jstor.org/stable/2044374?seq=4#metadata_info_tab_contents

@book{FHT,
author = {Yves Félix and Stephen Halperin and Jean-Claude Thomas},
title= {Rational Homotopy Theory},
publisher= {Springer-Verlag},
year={2001}
}

@article{hess,
author = {Kathryn Hess},
year = {2007},
title = {Rational homotopy theory: a brief introduction},
volume = {436},
journal = {Interactions between Homotopy Theory and Algebra, Contemporary Mathematics},
pages = {175-202}
}
% https://homepages.math.uic.edu/~bshipley/hess_ratlhtpy.pdf





%%% Historical overview of A-infinity algebras

@article{keller,
author={Bernard Keller},
title={Introduction to A-infinity algebras and modules},
journal={Homology, homotopy and applications},
volume={3},
year=2001,
pages={1-35}
}
%https://arxiv.org/pdf/1209.3226.pdf

@book{h-spaces,
author = {James Stasheff},
year = {1970},
title = {H-spaces from a homotopy point of view},
journal = {Springer, Lecture notes in mathematics},
number ={161}
}
% https://link.springer.com/content/pdf/10.1007%2FBFb0065896.pdf

@article{h-spaces1,
author = {James Stasheff},
year = {1963},
title = {Homotopy associativity of H-spaces, I},
journal = {Transactions of the American Mathematical Society},
pages = {275–292},
volume = {108},
}

@article{h-spaces2,
author = {James Stasheff},
year = {1963},
title = {Homotopy associativity of H-spaces, II},
journal = {Transactions of the American Mathematical Society},
pages = {293–312},
volume = {108},
}

@book{adams_loop,
author = {John Frank Adams},
year = {1978},
title = {Infinite loop spaces},
publisher = {Hermann Weyl lectures at IAS, Annals of Mathematics},
number = {90},
}

@book{may_loop,
author = {James Peter May},
title= {The geometry of iterated loop spaces},
year={1972},
publisher= {Springer, Lecture notes in mathematics},
number={271},
}

@book{boardman_vogt,
author = {J.M. Boardman and R.M. Vogt},
title= {Homotopy invariant algebraic structures on topological spaces},
publisher= {Springer, Lecture notes in mathematics},
number={347},
year={1973}
}

@article{kontsevich,
author = {Maxim Kontsevich},
year = {1994},
title = {Homological Algebra of Mirror Symmetry},
journal = {Proceedings of the International Congress of Mathematicians},
pages = {120-139},
volume = {90},
}


@article{infty-massey,
title={Massey Product and Twisted Cohomology of A-infinity Algebras}, 
author={Weiping Li and Siye Wu},
year={2009},
volume={0912.1775},
journal={arXiv},
primaryClass={math.AT}
}
% https://arxiv.org/pdf/0912.1775.pdf




%%% Historical overview of DG-algebras

@article{situs,
author = {Henry Poincaré},
year = {1895},
title = {Analysis situs},
volume = {1},
journal = {Journal de l'École Polytechnique},
pages = {1-123}
}

@article{situs2,
author = {Henry Poincaré},
year = {1899},
title = {Complément à l'Analysis Situs},
volume = {13},
journal = {Rendiconti del Circolo Matematico di Palermo},
pages = {285–343}
}

@article{riemann,
author = {Bernhard Riemann},
year = {1857},
title = {Theorie der Abel’schen Funktionen},
volume = {},
journal = {Journal fur die reine und angewandte Mathematik},
pages = {101–155}
}

@article{betti,
author = {Enrico Betti},
year = {1870},
title = {Sopra gli spazi di un numero qualunque di dimensioni},
volume = {4},
journal = {Annali di Matematica Pura ed Applicata},
pages = {140–158}
}

@article{noether,
author = {Emmy Noether},
year = {1925},
title = {Ableitung der Elementarteilertheorie aus der Gruppentheorie},
volume = {34},
journal = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
pages = {104}
}

@article{mayer,
author = {Walther Mayer},
year = {1929},
title = {Über Abstakte Topologie},
volume = {36},
journal = {Monatshefte für Mathematik und Physik},
pages = {1-42}
}

@article{mayer2,
author = {Walther Mayer},
year = {1929},
title = {Über Abstakte Topologie II},
volume = {36},
journal = {Monatshefte für Mathematik und Physik},
pages = {219-258}
}

@article{whitney,
author = {Hassler Whitney},
year = {1937},
title = {On products in a complex},
volume = {23},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
pages = {285-291}
}

@book{history1,
author = {William S. Massey},
title= {The history of topology, Chapter 21: A history of cohomology theory},
publisher= {Elsevier B.V.},
year={1999}
}

@book{history2,
author = {Charles A. Weibel},
title= {The history of topology, Chapter 28: The history of homological algebra},
publisher= {Elsevier B.V.},
year={1999}
}




%%% Lusternik-Schnirelman category

@article{lscat,
author = {Lazar Lusternik and Lev Schnirelmann},
year = {1934},
title = {Methodes Topologiques dans les Problemes Variationnels},
journal = {Hermann, Paris},
}

@article{Rudyak,
author={Yuli B. Rudyak},
title={On category weight and its applications},
journal={Topology 38},
volume={1},
year=1999,
pages={37–55}
}
%https://hopf.math.purdue.edu/Rudyak/LScategory.pdf

@book{lscategorybook,
author = {Octav Cornea and Gregory Lupton and John Oprea and Daniel Tanré},
title= {Lusternik-Schnirelmann category},
publisher= {Mathematical Surveys and Monographs},
year={2003},
volume={103},
}




%%% Other 

@book{operads,
author = {Jean-Louis Loday and Bruno Vallette},
title= {Algebraic operads},
publisher= {Springer-Verlag},
year={2012}
}

@book{hatcher,
author = {Allen Hatcher},
title= {Algebraic topology},
publisher= {Cambridge university press},
year={2001}
}