@Preamble{"\def\cprime{$'$} "} @misc{LT, title={Robertson's conjecture I. Well-quasi-ordering bounded tree-width graphs by the topological minor relation}, author={Liu, Chun-Hung and Thomas, Robin}, eprint={2006.00192}, year={2020} } @article {RSXX, AUTHOR = {Robertson, Neil and Seymour, P. D.}, TITLE = {Graph minors. {XX}. {W}agner's conjecture}, JOURNAL = {J. Combin. Theory Ser. B}, FJOURNAL = {Journal of Combinatorial Theory. Series B}, VOLUME = {92}, YEAR = {2004}, NUMBER = {2}, PAGES = {325--357}, } @article{KR, AUTHOR = "Ben Knudsen and Eric Ramos", TITLE = "Geometric Filtrations in Graph Configuration Spaces (working title)", JOURNAL = "in preparation", YEAR = "2022", } @article{AK, title={On the second homology of planar graph braid groups}, author={An, Byung Hee and Knudsen, Ben}, journal={Journal of Topology}, volume={15}, number={2}, pages={666--691}, year={2022}, publisher={Wiley Online Library} } @misc{MR, title={The graph minor theorem in topological combinatorics}, author={Miyata, Dane and Ramos, Eric}, eprint={2012.01679}, year={2020} } @article{KP, AUTHOR = {Ko, Ki Hyoung and Park, Hyo Won}, TITLE = {Characteristics of graph braid groups}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {48}, YEAR = {2012}, NUMBER = {4}, PAGES = {915--963}, } @article {PR-trees, AUTHOR = {Proudfoot, Nicholas and Ramos, Eric}, TITLE = {Functorial invariants of trees and their cones}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {25}, YEAR = {2019}, NUMBER = {4}, PAGES = {Paper No. 62, 28}, } @article{PR-genus, title={The contraction category of graphs}, author={Proudfoot, Nicholas and Ramos, Eric}, journal={Representation Theory of the American Mathematical Society}, volume={26}, number={23}, pages={673--697}, year={2022} } @misc{A, AUTHOR = {Abrams, Aaron David}, TITLE = {Configuration spaces and braid groups of graphs}, NOTE = {Thesis (Ph.D.)--University of California, Berkeley}, PUBLISHER = {ProQuest LLC, Ann Arbor, MI}, YEAR = {2000}, } @article{sam, AUTHOR = {Sam, Steven V and Snowden, Andrew}, TITLE = {Gr\"obner methods for representations of combinatorial categories}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {30}, YEAR = {2017}, NUMBER = {1}, PAGES = {159--203}, } @misc{Barter, title={Noetherianity and rooted trees}, author={Barter, Daniel}, eprint={1509.04228}, year={2015} } @incollection{Farley, Author = {Farley, Daniel}, TITLE = {Homology of tree braid groups}, BOOKTITLE = {Topological and asymptotic aspects of group theory}, SERIES = {Contemp. Math.}, VOLUME = {394}, PAGES = {101--112}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2006}, } @inproceedings{Knu, title={The topological complexity of pure graph braid groups is stably maximal}, author={Knudsen, Ben}, booktitle={Forum of Mathematics, Sigma}, volume={10}, pages={e93}, year={2022}, organization={Cambridge University Press} } @article{FS, AUTHOR = {Farley, Daniel and Sabalka, Lucas}, TITLE = {Discrete Morse theory and graph braid groups}, JOURNAL = {Algebr. Geom. Topol.}, VOLUME = {5}, YEAR = {2005}, PAGES ={1075--1109}, } @misc{Saw, title={Topology of graph configuration spaces and quantum statistics}, author={Sawicki, Adam}, eprint={1408.7002}, year={2014} } @article{AG, title={Finding topology in a factory: configuration spaces}, author={Abrams, Aaron and Ghrist, Robert}, journal={The American mathematical monthly}, volume={109}, number={2}, pages={140--150}, year={2002}, publisher={Taylor \& Francis} } @article {arnold, AUTHOR = {Arnol'd, V. I.}, TITLE = {The cohomology ring of the group of dyed braids}, JOURNAL = {Mat. Zametki}, FJOURNAL = {Akademiya Nauk SSSR. Matematicheskie Zametki}, VOLUME = {5}, YEAR = {1969}, PAGES = {227--231}, } @article{Sw-graphs, AUTHOR = {\'Swi\k{a}tkowski, Januszkiewicz}, TITLE = {Estimates for homological dimension of configuration spaces of graphs}, JOURNAL = {Colloquium Mathematicum}, VOLUME = {89}, YEAR = {2001}, PAGES = {69--79}, } @article{CL, AUTHOR = {Chettih, Safia and L\"utgehetmann, Daniel}, TITLE = {The homology of configuration spaces of trees with loops}, JOURNAL ={Algebraic \& Geometric Topology}, VOLUME = {18}, YEAR = {2018}, PAGES ={2443--2469}, }