641 Women in Topology: Collaborations in Homotopy Theory WIT: Women in Topology Workshop August 18–23, 2013 Banff International Research Station Banff, Alberta, Canada Maria Basterra Kristine Bauer Kathryn Hess Brenda Johnson Editors American Mathematical Society 641 Women in Topology: Collaborations in Homotopy Theory WIT: Women in Topology Workshop August 18–23, 2013 Banff International Research Station Banff, Alberta, Canada Maria Basterra Kristine Bauer Kathryn Hess Brenda Johnson Editors American Mathematical Society Providence, Rhode Island Editorial Board of Contemporary Mathematics Dennis DeTurck, managing editor Michael Loss Kailash Misra Martin J. Strauss 2010 Mathematics Subject Classification. Primary 18D50, 18G55, 18G60, 22A22, 55N91, 55P91, 55U15, 55U35, 57R18. Library of Congress Cataloging-in-Publication Data Women in topology : collaborations in homotopy theory : Workshop on WIT, Women in Topol- ogy : August 18-23, 2013, Banff International Research Station, Banff, AB, Canada / Maria Basterra, Kristine Bauer, Kathryn Hess, Brenda Johnson, editors. pages cm. – (Contemporary mathematics ; volume 641) Includes bibliographical references. ISBN 978-1-4704-1013-1 (alk. paper) 1. Homotopy theory–Congresses. 2. Topology–Congresses. 3. Women in mathematics–Con- gresses. I. Basterra, Maria, 1964– editor. II. Bauer, Kristine, 1973– editor. III. Hess, Kathryn, 1967– editor. IV. Johnson, Brenda, 1963– editor. QA612.7.W66 2013 514.2409252–dc23 2014046384 Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online) DOI: http://dx.doi.org/10.1090/conm/641 Copying and reprinting. 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Copyright ownership is indicated on the copyright page, or on the lower right-hand corner of the first page of each article within proceedings volumes. c 2015 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Copyright of individual articles may revert to the public domain 28 years after publication. Contact the AMS for copyright status of individual articles. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10987654321 201918171615 Contents Preface v List of Participants vii Representations of Derived A-infinity Algebras Camil I. Aponte Roman,´ Muriel Livernet, Marcy Robertson, Sarah Whitehouse, and Stephanie Ziegenhagen 1 Unbased Calculus for Functors to Chain Complexes Maria Basterra, Kristine Bauer, Agnes` Beaudry, Rosona Eldred, Brenda Johnson, Mona Merling, and Sarah Yeakel 29 Left-Induced Model Structures and Diagram Categories Marzieh Bayeh, Kathryn Hess, Varvara Karpova, Magdalena Ke¸dziorek, Emily Riehl, and Brooke Shipley 49 Fixed Points of p-Toral Groups Acting on Partition Complexes Julia E. Bergner, Ruth Joachimi, Kathryn Lesh, Vesna Stojanoska, and Kirsten Wickelgren 83 On the Higher Topological Hochschild Homology of Fp and Commutative Fp-Group Algebras Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, and Inna Zakharevich 97 A Model Structure on GCat Anna Marie Bohmann, Kristen Mazur, Angelica´ M. Osorno, Viktoriya Ozornova, Kate Ponto, and Carolyn Yarnall 123 Orbispaces and Their Mapping Spaces via Groupoids: A Categorical Approach Vesta Coufal, Dorette Pronk, Carmen Rovi, Laura Scull, and Courtney Thatcher 135 iii Preface Women in Topology (Banff 2013) was the first workshop organized by the newly founded network WIT–HT (Women in Topology–Homotopy Theory), in an endeavor to increase the number and visibility of active female researchers in ho- motopy theory. Modeled on the successful five-day workshops organized by the Women in Numbers network in 2008 and 2011 at the Banff International Research Station, the WIT workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students, on projects prepared by the team leaders. Our goal in organizing this workshop was to support and expand research activity of women in the field of homotopy theory, by contributing to the training of graduate students and by fostering collaborations amongst female researchers. The publication of the findings of each workshop team in this proceedings volume is an important milestone in this process, but not the end of the road: many of the workshop teams are actively continuing their collaboration. We are deeply grateful for the generous support of the Banff International Research Station and of the Clay Mathematics Institute’s Enhancement and Part- nership program, which funded travel for our participants. We thank the Pacific Institute for Mathematical Sciences and the Ecole Polytechnique F´ed´erale de Lau- sane for additional support. Maria Basterra Kristine Bauer Kathryn Hess Brenda Johnson v List of Participants Camil I. Aponte Rom´an Kathryn Lesh University of Washington Union College Maria Basterra Ayelet Lindenstrauss University of New Hampshire Indiana University Kristine Bauer Muriel Livernet University of Calgary Universit´e Paris 13 Marzieh Bayeh Kristen Mazur University of Saskatchewan Lafayette College Agn`es Beaudry Mona Merling University of Chicago Johns Hopkins University Julia E. Bergner Ang´elica M. Osorno University of California-Riverside Reed College Irina Bobkova Viktoriya Ozornova Northwestern University Universit¨at Bremen Anna Marie Bohmann Kristine Pelatt Northwestern University St. Catherine University Vesta Coufal Kate Poirier Gonzaga University CUNY Rosona Eldred Kate Ponto Universit¨at M¨unster University of Kentucky Kathryn Hess Dorette Pronk EPFL Dalhousie University Ruth Joachimi Birgit Richter Universit¨at Wuppertal Universit¨at Hamburg Brenda Johnson Emily Riehl Union College Harvard University Varvara Karpova Marcy Robertson EPFL University of Western Ontario Magdalena K¸edziorek Carmen Rovi University of Sheffield University of Edinburgh vii viii PARTICIPANTS Laura Scull Fort Lewis College Brooke Shipley University of Illinois at Chicago Vesna Stojanoska MIT Courtney Thatcher Bard College at Simon’s Rock Sarah Whitehouse University of Sheffield Kirsten Wickelgren Georgia Institute of Technology Carolyn Yarnall Wabash College Sarah Yeakel University of Illinois at Urbana-Champaign Inna Zakharevich Institute for Advanced Study Stephanie Ziegenhagen Universit¨at Hamburg Participants at the Women in Topology (Banff 2013) Workshop CONM 641 Women in Topology This volume contains the proceedings of the WIT: Women in Topology Workshop, held from August 18–23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homo- • topy theory, including A-infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology. Basterra et al., Editors ISBN 978-1-4704-1013-1 9 781470 410131 CONM/641 AMS.