By Gail Letzter, Kristin Lauter, Erin Chambers, Nancy Flournoy, Julia Elisenda Grigsby, Carla Martin, Kathleen Ryan, Konstantina Trivisa

ISBN-10: 3319341375

ISBN-13: 9783319341378

ISBN-10: 3319341391

ISBN-13: 9783319341392

Providing the newest findings in themes from around the mathematical spectrum, this quantity contains leads to natural arithmetic besides quite a number new advances and novel functions to different fields corresponding to chance, facts, biology, and desktop technological know-how. All contributions characteristic authors who attended the organization for ladies in arithmetic study Symposium in 2015: this convention, the 3rd in a sequence of biennial meetings equipped through the organization, attracted over 330 members and showcased the study of girls mathematicians from academia, undefined, and government.

**Read or Download Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium PDF**

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**Extra resources for Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium**

**Example text**

Critical point switches (Yα , Yβ ), (Yβ , Yα ) and (Yα− , Yβ ), (Yβ , Yα − ) occur for disjoint attaching cycles α, β ⊂ Σ; these give rise to a pair of cobordisms17 ≥ 2 when discussing connected bordisms since the handle attachments in dimension d = 1 are morphisms between generally disconnected 1-manifolds, so that Bor conn 1+1 does not have useful connected Cerf decompositions. 1 for more details on the notation used here. 16 We restrict to dimension d 18 K. Wehrheim Fig. 4 Cerf decompositions of a 3-cobordism Y and Cerf moves between them Yα ∈ Mor(Σ, Σα ), Yβ ∈ Mor(Σα , Σ ) whose composition is the same as that of the pair Yβ ∈ Mor(Σ, Σβ ), Yα ∈ Mor(Σβ , Σ ).

Take |I|([Y ]) to be the isomorphism class of the Floer homology HF(LH0 , LH1 ). 4. Check that different choices of representatives and Heegaard splittings yield isomorphic Floer homology groups. The last step of this program is a major challenge. , is independent—up to isomorphism—from other choices involved in the construction. 6, the invariance in Step 4 was proven as part of the construction [52], but also follows from the analogue of the Atiyah–Floer conjecture established in [35], which identifies the three flavors of Heegaard Floer homology with three flavors of monopole Floer homology.

Y , Zφ ), Y in which Y is the same cobordism as Y (up to diffeomorphism), but with incoming resp. outgoing boundary inclusion pre- resp. post-composed with a diffeomorphism φ. – Critical point cancellations (Yα− , Yβ ), Zφ occur for attaching cycles α, β ⊂ Σ with transverse intersection in a single point; these give rise to a pair of cobordisms Yα− ∈ Mor(Σ , Σ), Yβ ∈ Mor(Σ, Σ ) whose composition is a cylindrical cobordism representing a diffeomorphism φ : Σ → Σ . – Critical point switches (Yα , Yβ ), (Yβ , Yα ) and (Yα− , Yβ ), (Yβ , Yα − ) occur for disjoint attaching cycles α, β ⊂ Σ; these give rise to a pair of cobordisms17 ≥ 2 when discussing connected bordisms since the handle attachments in dimension d = 1 are morphisms between generally disconnected 1-manifolds, so that Bor conn 1+1 does not have useful connected Cerf decompositions.

### Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium by Gail Letzter, Kristin Lauter, Erin Chambers, Nancy Flournoy, Julia Elisenda Grigsby, Carla Martin, Kathleen Ryan, Konstantina Trivisa

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